Learn About Stem and Leaf Plots and Measures of Central Tendency

TenMarks teaches you about stem and leaf plots and measures of central tendency.

In this lesson let’s learn how to use Stem and Leaf Plots to compute Measures of Central Tendency. Again, measures of central tendency are Mean, Median, Mode etcetera. So first, let’s do a stem and leaf plot. We draw our steam and the leaves. How do we do this? We look at the lowest value—15; highest value—45; both have two digit numbers, tens digit, one is tens and ones. So we start with stems 1, 2, 3, 4—tens, twenties, thirties and forties. Once I’ve got 15 and that’s it. Twos, what numbers do we have starting with 20? We’ve got all of this; so we’ve got 2 and 6, 2 and 6, 2 and 7, 2 and 8, 2 and 9 and 2 and 9. Thirties, I’ve got 3 0, 3 2, 3 3, 3 5, 3 6, 3 8, 3 8 and 3 8; four I’ve got 4 0, 4 1, 4 2, 4 3 and 4 5. That’s my stem and leaf plot. First part of the question is wants us to draw vertical segments on the plot to indicate the Median and the first and third quartiles. Let’s learn how to find Medians. Well I’ve got 20 values in here, so the Median will be the Mean of 10th and 11th values. The Median has the middle value, so if we have 20 values—well obviously there’s ten above, ten below which means there’s nothing in the middle. So I’ve got to take the middle two values; I leave 9 values above; 9 values below; these are the two middle values. So I add 33 plus 35 over two which is 16 over 2 or 34. I could’ve done it here as well—1, 2, 3, 4, 5, 6 ,7, 8, 9—9 values up; 1, 2, 3, 4, 5, 6, 7,8, 9—9 values below. The Median is the Mean of these two values—33 and 35, exact same thing. So the Median is 34. What’s the 1st and 3rd quartile? Well if the Median, which is right here, divides the data set in to two halves—this is the upper half; this is the lower half. The first quartile is the middle value of the upper half. So again I’ve got 10 values which means that the 5th and 6th—the Mean of which will be the Median of this set. So imagine if these were two sets of numbers—10 above, 10 below. So what’s the Median of this set? It’s the equal—the Mean of these two numbers—4 above, 4 below. So the 1st quartile is 28 plus 29 over two which is 28.5. The third quartile is doing the same thing here; so the 4 values below, 4 values above, which means 38 and 40. Which is 39? So the 1st quartile and the 3rd quartile; essentially all that means is the Median is the center value which would be right here. Then the first quartile is right here; the third quartile is right here. If we will divide this into four equal halves or equal quarters, 1st quartile would be average or the middle value between the 1st and 2nd; 2nd, the Median would be between the 2nd and 3rd; 3rd quartile would be between 3rd and 4th , that makes sense. Now let’s look at the other problems. Well that’s it, that’s all we have to do. Draw vertical segments to indicate the Median and the first and third quartile. So let’s recap what we’ve learned. When we drew a data set, we can draw a stem and leaf plot by simply writing the tenths digit on the left and ones digit on the right, and we get all 20 values. Now in this example it’s tens and ones because that’s the variety numbers; they’re all two digit numbers. Then we have to compute the Mean of tenth and eleventh values to get the Median. The Median is the center value; if there are 20 numbers, well the center value is not one number but two numbers because there’s nine numbers above, numbers below it. So if we get two numbers at the middle, we take the average of them to get it. Similarly, if the top half has got ten numbers—this is the top half, the Mean of the middle two values is called the first quartile; Mean of B; middle two values of D; lower half is called the 3rd quartile.