Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find the mean, median, mode, and mid-range for converted categorical data.  Here's our problem statement: Find the mean, median, mode, and mid-range for the given sample data.  An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas.  Listed below are the phenotype codes where 1 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow, and 4 = wrinkled-green.  Do the results make sense?

OK, the first part here is asking us to find the mean.  This is really easy to do in StatCrunch.  But first we need to load our data into StatCrunch.  So I'll click on this icon and open in StatCrunch.  Here's my data in StatCrunch.  I'm gonna resize this window so you can see more of what's going on.  There we go.

OK, so to find the mean, I need to take — that's a statistic of this column, so I'm going to go to Stat –> Summary Stats –> Columns.  I select the column where my data is located.  And then down here under Statistics, I select the mean.  I hit Compute!, and there is my mean value.  I'm asked to round to the nearest tenth.  Nice work!

And now the second part asks me for the median.  So I could go through those menu options again, but it's much simpler if I just click on this Options button and click on Edit.  And now I just go and find the median, hit Compute!, and there my results window changes to include the median.  Nice work!

The third part asks for the mode.  So I go back into my options window.  Mode is located towards the bottom here.  Excellent!

Mid-range — so then I go back into my options window.  And you can go up and down this list, but you're not gonna find mid-range.  How then do we get the mid-range using StatCrunch?  Well, we have to kind of go through it the back door, so to speak.  We can get the range, and then I'm gonna select the min.  But I need to select both of those values, so I'm gonna hit the Ctrl button on my keyboard while I select the second statistic.  So now I got both of these.  That will pop up in my results window.

OK, so the range is 3, and the minimum value is 1.  So I take half the range — and half of 3 is 1.5 — and I add it to the min.  1.5 + 1 = 2.5.  Fantastic!

Now the last part of this problem asks, “Do the measures of center make sense?”  Well, you can go through and look at the different answer options here.  Or if we go back and look at how the data were actually established, we see that, even though the data is composed of numbers, these numbers are really categorical data because that's how they're defined.  The 1, the 2, the 3, the 4 — they're really labels to represent the different types of peas according to how the soil affects the phenotype.

So these are categorical data.  And when you're dealing with categorical data, the mean doesn't make sense.  The median doesn't make sense.  Only the mode as a measure of center makes sense when dealing with categorical data.  So I look at my answer options, and it looks like this one matches that sort of thinking.  Well done!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I’m Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to identify critical R values.  Here's our problem statement: For a data set of brain volumes and IQ scores of six males, the linear correlation coefficient is R = 0.568.  Use the table available below to find the critical values of R based on a comparison of the linear correlation coefficient R and the critical values.  What do you conclude about a linear correlation?

OK, the first part asks us to identify the critical values.  You notice that there are two critical values.  If I click here on this table, I'm only seeing one of the critical values.  OK, there are actually two critical values; one is positive and one is negative.  Only the positive one is listed here.

So the next question we have to ask then is to identify which critical value of R we want?  First, we need to look at the number of pairs of data that we have.  So in our data set it says that we have six males.  So therefore, I know I'm going to be looking at 6 here on the chart, and then come over to the right, and this value right here — 0.818 — is the critical value R for a data set with six pairs of data.

This then becomes a threshold value that we compare with the R value obtained from the actual data.  If the R value from the actual data is greater than this critical value, then we're in the clear, and we can say that we have we have enough evidence to conclude there's a linear correlation.  However, if the value we get for our from the data is less than this threshold value, then we don't have that evidence; we can't conclude that there is a linear correlation.  So it's pretty easy if you're just comparing absolute values of everything.  So let's go ahead and make that comparison here.  The R-value we get from our data is 0.568.  That is less than 0.811, so therefore we can't make that conclusion of linear correlation.

However, this first part is asking us for the critical values.  So we're gonna put those in here.  Remember there are two critical values; one is positive, one is negative.  There's two ways to input the answer.  I just like coming down here and pressing on this plus-or-minus button and then putting in the value that I got from the table.  But if you want you could actually list out the two numbers and separate them out with a comma.  So you could have -0.811, comma, and then 0.811 for the positive.  But I like this because it's just a little bit shorter.  Nice work!

And now the second part of our problem is asking us to interpret those critical values with respect to our data set.  So here we're saying that the correlation coefficient R and here they're actually relating it to a distribution, which we'll get into a lot more later on in the course.  But which one do we actually choose?  Well, since the R-value that we got from our data is less than the critical value for the positive — OK?  We're just comparing positives to each other, OK?  So that means we're gonna select “between the critical values.”  If this were a negative value and the R-value from the data set was greater than — well, greater absolute value; it's more negative than the negative, or it's more positive than the positive critical value — then we would say that it is below the negative or above the positive.  But that's not what we have here, so we're just going to select “between the critical values” and because we're in that region there is not sufficient evidence to support the claim of a linear correlation.

If we were in, say, one of those tail regions where we're much less than the negative or greater than the positive critical value, then, yes, we would be able to say that.  But as it is, this is what we have.  So I check my answer.  Good job!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to identify and interpret a p-value for a linear correlation.  Here's our problem statement: For a data set of brain volumes and IQ scores of 10 males, the linear correlation coefficient is found, and the p-value is 0.761.  Write a statement that interprets the p-value and includes a conclusion about linear correlation.

OK, here we have a statement that we're going to write.  There's three different blanks that we need to fill in the statement.  Let's take a look at the first one.

So here it says, “The p-value indicates that the probability of a linear correlation coefficient that is at least as extreme is blank percent.”  Well, this statement right here — probability of a linear correlation coefficient that is at least as extreme — this is a definition of the p-value.  Well, they give us the p-value here in the problem statement — 0.761.  Therefore, these two must be the same.  If this is the definition (which it is) and this is a numerical value for the same thing, then these must be the same thing.  So I'm going to take this p-value here and convert from decimal to percent.  To do that, I just move the decimal place two points to the right — 76.1%.

Let's look at the second blank here.  We're asked to say whether this p-value is high or low.  Well, this means we need to have a standard by which to judge.  And typically the standard or threshold that's used to judge is the level of confidence, represented with the lowercase Greek letter alpha.  We're not given anything like that in the problem statement, and therefore it's pretty safe to assume that we should just adopt the most commonly used threshold value.  And that is by far and away 5%.  So 76% is much much greater than 5%, so this is going to be high.

And then, with a high p-value, we're looking to see is there or is there not sufficient evidence to make our conclusion.  Well, a high p-value typically means you're over that threshold.  And if you're over the threshold, then there is not sufficient evidence to make your conclusion.  If you were under the threshold — in other words, the p-value is low, so you're below that threshold — then you would have sufficient evidence to make your conclusion.  But that's not the case here.  Our p-value is really high, and so there is not sufficient evidence to make our conclusion.  I check the answer.  Well done!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to construct a frequency polygon in StatCrunch.  Here's our problem statement: The given data represent the number of people from a town age 25 to 64 who subscribed to a certain print magazine.  Construct a frequency polygon.  Does the graph suggest that the distribution is skewed?  If so, how?

OK, the first thing we need to do for this first part that's asking us to construct the frequency polygon is take the data and put it into StatCrunch.  So here I've got my data in StatCrunch.  And I'm going to resize this window so we can see the better everything that's going on.  Excellent.

OK, now before we actually go and make the frequency polygon, we need to manipulate our data set a little bit.  We can't just dump this in.  We could, but we'll end up with something that's only partially correct.  The frequency polygon is constructed by looking at the midpoints for each of your classes or categories here.  And so it's almost like you're making a bar graph, but you're putting the dot at the midpoint on the top of each of the bars on your graph.  So we need to change these age limits a little bit.

And we also need to add in a couple of new categories, because the frequency polygon they want you to construct, it includes not just the data they give you but also the category before and the category after the data that they give you.  So we need to go ahead and put that into our data set here.

To do that I'm going to click on this little arrow and say Insert 1 Above.  And then the midpoint — I need to replace all of these ages with midpoints.  OK, so what's the midpoint for this first category?  Well, I just simply — if I take my calculator, I'm going to take the upper limit, subtract out the lower limit, divide by 2, and then add that to my lower limit.  So there's my midpoint.  I need to replace this first category with 29.5.

And then I can do the same calculation here.  Notice how it's apart by ten.  Notice how categories here — the lower limits are separated by 10.  The upper limits are separated by tens, so it only makes sense that the midpoints are gonna be separated by 10.  So I can just add 10 to the one that came before to get the next one in line.  And of course, for this column here that’s after the data set, I just add another 10.  And then for this column before the first category given in my data set, I'm gonna subtract 10 out.  And there's no data in either of those categories, so I'm just going to put zeros there.

OK, now I'm ready to actually make my frequency polygon.  To do that, I go to Graph and for this I'm gonna go Chart –> Columns.  Here in the options window, I want to select People, because this is where the actual frequency counts are located.  And then down here, I want to put under Plot, I want to select “points with connected lines.”  All the other default options are good for our purpose, so we'll just hit Compute!.  And I've got the basic shape for my frequency polygon here.  So it's going to match up with Answer option C.

If I really wanted to get the label on the x-axis correct, I mean, I could always go back to my options window and say the row labels are in Age.  And now the numbers actually match up with what you see here in your answer option.  So I'm going to check my answer.  Nice work!

Now the second part of this problem asks, “Does the graph suggest that the distribution is skewed?  If so, how?”  Well, just look at your graph.  It's not symmetrical.  It's actually — all the data is just pushed over here on the right.  So my friends in industry and I would say this is skewed to the right.  But since this question in your assignment is made by a pure statistician, they look for where the longer tail is.  And that's going to be here on the left, so we're gonna say that the distribution appears to be skewed to the left.  Good job!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find probability by subjective judgment.  Here's our problem statement: Assume that 700 births are randomly selected and 341 of the births are girls.  Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.

OK, we have four different options from which to choose.  How do we know which option is the correct one?  Well, we're looking at births, and a birth could be either a boy or a girl.  So we would expect that the number of births that are girls would be approximately half of the total amount, because there's approximately a 50% chance of having a birth be a girl if everything is truly randomly selected.  So we would expect about half of the 700 to be girls.  And indeed, we see that 341 is around 350, which is half of 700.  So we would say, yes, that the number of girls is neither significantly low nor significantly high.

Another way to get the answer is to actually use your calculator.  I know it says “subjective judgment,” but we can actually run the numbers out.  The probability from this sampling is the part over the whole.  So we have the part, which is 341, and divided by the whole, which is 700, and here we've got a little bit more than 48% of the the sample here are girls.  This is around 50%, so again we would say that the number of girls is neither significantly low nor significantly high.

How far away could you get from that 50% expected probability before you start saying, “OK, so now the difference is statistically significant”?  Well, you need a standard to go by, and the standard that's typically used is 5%.  There is no mention in the problem statement of what standard to use because they want you to use subjective judgment.  However, in those cases where they don't mention anything, it's by and large your best bet to just use the standard that is by and far the most commonly used, and that is 5%.

So here we see we're expecting 50%.  We have a little more than 48%, so if you subtract that out, you're gonna get less than 5%.  So we're within that 5% margin, and so we would say that, yeah, this is within what we would expect to see; it's not significantly low or significantly high.  Well done!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to construct a histogram from a frequency distribution table.  Here's our problem statement: The table shows the magnitudes of the earthquakes that have occurred in the past 10 years.  Use the frequency distribution to construct a histogram.  Does the histogram appear to be skewed?  If so, identify the type of skewness.

OK, the first part of our problem asks us to construct the histogram.  So to do that I'm going to take my data here and dump it into StatCrunch.  I'm going to resize this window so we can see a little bit better what's going on.  OK, now my data is here in StatCrunch.

You would think that, to construct a histogram, you would go up to Graph and then select Histogram.  However, the data that you have in your data table are frequency counts from a frequency distribution table.  The histogram functionality in StatCrunch is ... has a default setting which is designed to take raw data that hasn't yet been assembled into a frequency distribution table and then make the histogram from that.  Because you already have the data in a frequency distribution table, if you try to use the histogram function, you're going to get something that looks very, very funky.  It will count each one of these numbers as one count.  So instead of the first category having 12 counts, it will only count one.  So you have this basic uniform distribution which is nothing like the actual histogram that you're trying to construct.

How then do we use StatCrunch with a frequency distribution table to get our histogram?  Well now, look at this option right above Histogram.  It says Chart.  You want to go there, and then you want to click on Columns.  In the options window, you want to click on the column where your frequency counts are located.  And then the default is to assemble the plot with horizontal bars.  I don't know why they set that as the default, but since we're looking here for vertical bars, you want to go ahead and select “vertical bars (split)” as our plot option.

And now I'm ready to hit Compute! and, lo and behold, here's my histogram.  The numbers that you see here on the x- or horizontal axis do not correspond with the earthquake magnitudes.  That's OK; we're just looking here for the shape of our distribution inside the histogram.  So now we match what we have with our answer choices.  It looks like Answer choice D is gonna be the one we want.  Excellent!

And now the second part of our problem asks us about any skewness in the histogram that we've just constructed.  So to look for skewness, we're looking for a longer tail on either the right or the left.  This histogram is not roughly symmetric; there's a lot more data here on the left than there is on the right, so there's a longer tail here on the right section — hardly anything here on the left.  So this is going to have a longer tail on the right, and so the distribution will be (as a pure statistician would say) skewed to the right.

If you're asking my friends in industry, “How is this distribution skewed?” then they would say the same thing I would say.  It's skewed to the left because the left side of the distribution is where all the data is located.  But the questions that you’re asked in your assignments are created by a pure statistician, and pure statisticians don't look for where the data is when assessing skewness.  They look for where is the longer tail.  So here the longer tail is on the right, so we're gonna say it's skewed to the right.  Nice work!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find measures of variation before and after adding a data point.  Here's our problem statement: Use the magnitudes of Richter scale of the 120 earthquakes listed in the accompanying data table.  Use technology to find the range, variance, and standard deviation.  If another value (7.0) is added to those listed in the data set, do the measures of variation change much?

OK, the first part here is asking us to find the range.  To do that, I'm going to take my data set here and dump it into StatCrunch here.  And let's resize this window so we can see a little bit better what's going on.  There we go.  Now my data's here in StatCrunch.

So to find the range, I'm simply calculating a statistic for data that I have in my column.  And to do that, I go to Stat –> Summary Stats –> Columns.  I select the column where my data is located, and then here under Statistics, I'm just gonna select the statistic that they're asking for — in this case, the range.  Then I press Compute! and there's my range.  I'm asked to round to three decimal places, which in this case is no big deal.  Well done!

Now the next part asks me to find the standard deviation.  I could go through these menu options again, or I could just go up here to Options in my results window, and then in the drop down menu click Edit, and it takes me right back to the same options window where I can just select the new standard deviation that I want to calculate.  Notice in the list here, there are actually two variances and standard deviations.  OK, there’s two at the top, and then there's two here at the bottom (they're listed as unadjusted).  The unadjusted variety is for populations.  Here we're calculating a standard deviation for the sample, so we want to make sure that we select the standard deviation up here at the top, which we have.  I just press Compute!.  I'm asked to round to three decimal places.  Fantastic!

The next part asks me to calculate the variance, so I go back to my options window, switch over to the variance.  I'm asked to round to three decimal places again.  Nice work!

Now we're asked — with the extra data value — what is the range?  Well, notice how we're gonna go through the same — it looks like we're gonna go through the same three statistics to calculate, but this time we're adding in an extra data value, which from the problem statement is 7.0.  So first I need to come back over here to my data set, and I'm gonna scroll down here to the bottom, and then right here at the bottom I'm going to stick in that extra data point.

Now I go back to my options window, and I know I'm gonna have to calculate the same numbers again, so I'm just going to select them in the same order: the range, standard deviation, and the variance.  This time I don't have to keep going back and forth; I get everything I need for the rest of the problem here in one handy dandy results window.  And so I'm just going to take the numbers there off the results window.  And I'm asked again to round to three decimal places.  Good job!

Now the last part of this problem asks, “Do the measures of variation change much with the extra data value?”  If I look on these drop down boxes for the blanks that I'm supposed to fill in, notice how we're using five percentage points as the boundary between what's statistically significant and what's not.  So to determine whether the statistics that I've calculated up here fall into that, I'm just gonna pull up my calculator.

And here we're just gonna start with the range because that's what was asked for first.  So what's the change in the range from a percentage point of view?  Well, I'm going to take the difference between the two and then subtract it and — excuse me, divide — by the original amount.  So I'm going to start with 5.86, subtract out 3.6, and then I'm going to divide that by the original amount (3.6), and I get around 62%, which is well over 5%.  So this first one is going to be more than five percentage points.

I'm going to repeat the same calculation for the remaining statistics.  So the next one they have here is the variance.  So we go with 0.589, subtract out the original value point (0.427), and then divide it by the original amount.  Again, we're well over 5%, so that's going to be more here.  I'll do the same thing with my standard deviation values: 0767 minus 0.653, and then I'm going to divide that by 0.653.  And again, we're well over 5%.

So if they were within 5%, we could say they didn't really change much.  But they all changed by well more than 5%, so there are significant differences by adding in that extra data point.  So here in this last blank, we're gonna select “all of them change.”  Excellent!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find conditional probability from a frequency table.  Here's our problem statement: In an experiment, college students were given either four quarters or a $1 bill, and they could either keep the money or spend it on gum.  The results are summarized in the table.  Compare Parts A through C below.

OK, Part A asks us to find the probability of randomly selecting a student who spent the money given that the student was given four quarters.  Conditional probability is calculated by looking at the probability of both events occurring and then dividing that by the probability of just the one event occurring.  To do this, we can actually leave our data here in the table; we don't have to dump our data into any third party software.  I'm actually going to put the data into Excel because Excel makes it kind of nice for our purposes.  And I'll show you how nice it can be here in a moment.

You can work the problem in StatCrunch, but the problem with working in StatCrunch is that for this type of application, StatCrunch is actually pretty clunky and awkward.  You can do it, but because it's so awkward to use StatCrunch, I'm actually going to use Excel.  So we'll open up Excel here.

All right, here's my data here in Excel — whoa!  Oh, wow.  Yeah, OK, so that's a different problem.  Let's actually move you over here because I think — yes, that actually matches.  Hey, hey, where you going?  Stupid window!  Go where I want you to go!  Yeah, let's actually put you right here.  Yes, let's get rid of you.  What are you moving back here for?  Ah, ah, why can't you be where I want you to be?  Why are you trying to think for me?  Do what you're told!  OK, here we go.  Now we're ready.

So now I have the data here.  So we wanted to find the probability of randomly selecting a student who spent the money given that the student was given four quarters.  OK, well, first the probability of both — the probability that you both spent the money (which means you purchased the gum) and that you the student was given four quarters.  So four quarters is this row.  So the point where they both intersect is here at the 26.  So that's going to go on top.

So we're going to take 26, and we're gonna divide that by the probability that the student was given the four quarters.  Well, how many students were given the four quarters?  This is where Excel makes it really nice, because all I have to do is just select the cells for that given category (given the four quarters) and then down here Excel actually sums up everything really nice for me.   The sum is 42.

I can get the same thing in this calculator just by using the parentheses.  See, there's my 42 all the same.  But either way you work it, this is why I say you don't really need any third-party software; you just need to know which numbers to put in, and then you can actually get it out.  There's your probability.  I'm asked to round to three decimal places.  Fantastic!

Now, Part B asks us to find the probability of randomly selecting a student who spent the money given that the student was given a one dollar bill.  OK, so same calculation, but just slightly different numbers.  So again, we want to get the students who spent the money and was given the $1 bill.  So you spent the money and you were given the one dollar bill.  That's gonna be the 19.  So 19 divided by — and then how many were given the one dollar bill?  47.  There's my probability.  Again I'm asked to round to three decimal places.  Nice work!

And the last part, Part C, asks, “What do the preceding results suggest?”  Before we look at our answer options, let's go ahead and look at what the preceding results actually are.  So here we've got two probabilities.  They're both probabilities for students who spend the money, but the condition is the thing that's different between them.  So in this case, the probability that's higher is associated with having the four quarters as opposed to the dollar bill.  So what we see here is that, if you're gonna spend the money, it's more probable you'll spend it if you actually have four quarters as opposed to the dollar bill.

OK, let's go back and look at our answer options and see which one matches what we've just learned.  Answer option A says, “A student was more likely to have spent the money than to have kept the money.”  Well, we didn't do any probabilities with keeping the money, just the probabilities of students who spent the money.  So that's not going to be right.  Answer option B says, “A student given four quarters is more likely to have spent the money than a student given a $1 bill.”  And yes, that's what we learned just a moment ago.  So I'm going to select that.

But just to make sure, let's check the other answer options before we check our answer.  Answer option C says, “A student given a $1 bill is more likely to have spent the money.”  No, we don't — that’s not what this is saying right here; it's actually the reverse.  And then answer option D says, “A student was more likely to be given four quarters than a one dollar bill.”  Well, the problem statement doesn't say anything about how students were selected for each of the categories or groupings.  It just says that they were selected.  We presume that it's random, but we don't really know because there's nothing about it that's said in the problem statement.

So it looks like answer option B is the one we're going to go with.  Well done!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below to let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't care to help you learn stats, go to aspiremountainacademy.com, where you can find out more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find a five-number summary and construct a boxplot.  Here's our problem statement: Listed below our amounts of strontium-90 (in millibecquerels) in a simple random sample of baby teeth obtained from residents in a region born after 1979.  Use the given data to construct a boxplot and identify a five-number summary.

OK, here we have our data set, and the first part of this problem is asking us to construct a five-number summary.  This is really easy to do once we dump our data into StatCrunch.  So here's my data in StatCrunch.  I'm going to resize this window so we can see a little better what's gonna happen here.  Great!

Now, to get the five-number summary, I'm going to go into Stat –> Summary Stats –> Columns because I'm looking for summary statistics on data that are listed in a column.  I select the column where my data are located.  And then I come down here and select the specific statistics for the five-number summary.  To do that on an individual basis, I'm going to use the Ctrl-click option.  So I press the Ctrl button on my keyboard, and then with the left button on my mouse I'm going to click the individual statistics I want for my five-number summary.

What are the statistics for the five-number summary?  Well, if you need a review of that, here you go.  The five-number summary is the minimum, the first quartile, the median (which is also the second quartile), the third quartile, and the maximum.  So these are the numbers that I want to select for my five-number summary.

In order to put the answers in the proper order, I'm going to list them in the proper order when I calculate them in StatCrunch.  So the first one I want to select is the min.   So I come down here and select the min.  And then pressing the Ctrl button and keeping it pressed on my keyboard, I'm going to select the next four numbers for my five-number summary.  So after the min, we have the first quartile, and then the median, and then the third quartile, and then the minimum — excuse me — the maximum.

Notice how the numbers that I selected are listed here.  This is the order in which they will appear in the results window.  So if I select them in a different order, they'll appear in a different order.  This helps me to know what order the numbers are going to be in the results window before I select Compute!.  This is the order I want.  So now I'm going to go down here and click Compute!.

Now, here in my results window is my five-number summary, and it's in the order than I need to put them in the answer fields.  So I'm going to do that now.  Fantastic!

And now the second part of this problem asks us to construct a boxplot.  I can do that very easily in StatCrunch by going to Graph –> Boxplot.  Here I select the column where my data is located.  And then, for some reason, the default selection for StatCrunch is to draw the boxplot vertically.  But for all the homework assignments that you're going to have here, the boxplots are drawn horizontally.  So you want to come down here under Other options and click this box next to Draw boxes horizontally.

The other default options are fine for our purpose, so we're going to select Compute!.  And now here we have our boxplot.  So we just match the one that we drew with the right answer here.  And notice how we've got different numbers here on our axes.  We can change the numbers that are listed here on the axis if we wanted to.  Here I've got it set from about 120 to about 180 (it’s what it came up to be).  So let's see what matches here.  We've got the edge of our whisker a little to the left of 120, so that ... that ... so A and D are not going to be correct.  And I want — let's just go ahead and just change this axis here.  I want to go full-out to 180.  OK, see this whisker here on answer B; it goes almost to 200, but we're not even past 180 yet, so this has got to be the right answer here — answer option C.   And the edges of the boxes look good.  Everything seems to match up, so we're gonna select answer C.  Fantastic!

And that's how we do it at Aspire Mountain Academy.  Be sure to leave your comments below and let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching!  We'll see you in the next video.