Stem-and-Leaf Plots + Histograms + Back to Back Stem-and-Leaf Plot + Box-

and-Whisker Plot

By L.D.

Slide 3: Stem-and-Leaf Plots Slide 6: Mini Lesson: What If Slide 8: Mini Lesson Key 1 Slide 9: Mini Lesson: Key 2 Slide 10: Histogram Slide 12: Mini Lesson: The Difference Between Bar

Graphs and Histograms Slide 13: Back to Back Stem-and-Leaf Plot Slide 17: Box-and-Whisker Plot Slide 20: Mini Lesson: Box Position

Table of Contents

Example Problem: In the town of Sugar Pine, the next high

temperatures for the next ten days are below. 63 F°, 63 F°, 65 F°, 66 F°, 73 F°, 75 F°, 78 F°,

81 F°, 81 F°, 82 F° Now we need to look at all the different

numbers in the tenth place on the next slide.

Stem-and-Leaf Plots

63, 63, 65, 66, 73, 75, 78, 81, 81, 82 Now we need to look at all the different

numbers that aren’t in the one’s place, there is 6, 7 & 8. We will place these on one side of the line and place the numbers that were tied to those numbers on the other side of the line on the next slide.

Stem-and-Leaf Plots

6 3 3 5 6 7 3 5 8 8 112

Stem-and-Leaf Plots

Now that that is done, we need to give it the right format with a title, units and key. This will be on slide 7.

Note: There are not any spaces between the numbers.

If one of the temperatures had been 9 F° and

if one had been 134 F° and if one had been 3445 F°, it would have been looking like the below.

Mini Lesson: What If

0 91 343 445

6 3 3 5 6 7 3 5 8 8 112

High Temperatures For the Next Ten Days

(Degrees Fahrenheit)

Key: 6 I 3 = 63

A key can be ANY number in the problem.

Mini Lesson Key 1

A key tells you what is between the lines, an

example could be if you were working with decimals and you had the whole number on the left side and the other number on the other side. If your key number was 1.9 then the key would look like

1 I 9 = 1.9

Mini Lesson: Key 2

We will use the same set of numbers 63 F°, 63 F°, 65 F°, 66 F°, 73 F°, 75 F°, 78 F°,

81 F°, 81 F°, 82 F° We will arrange these on a graph, instead of

categories we will have number ranges, for this one I will use a number range of 10, the amount of numbers that fit into that range will add up on the bar.

Histogram

High Temperatures For the Next Ten Days

60 - 69 70 - 79 80 - 89

1

2

3

4

5

6

7

Frequency

(Degrees Fahrenheit)

Mini Lesson: The Difference Between Bar Graphs and

Histograms

The key differences are that the bars touch in a histogram and they don’t in a bar graph. Another example is that the categories on a bar graph are words and on a Histogram they are numbers.

The back to back stem-and-leaf plot shows the

prices (in dollars) of Poodles and Chihuahuas at a breeder. Compare the prices of adoption for the two dogs.

This plot is on the next page.

Back to Back Stem & Leaf Plot

Poodle3 1 07 5 58 7 6 5 48 8 5 5

Adoption Prices

4567

Chihuahua0 0 2 3 31 1 2 3 5 50 2 22

Key: 4 I 6 I 0 = $64, $60

Poodle3 1 07 5 58 7 6 5 48 8 5 5

Back to Back Stem & Leaf Plot

4567

Chihuahua0 0 2 3 31 1 2 3 5 50 2 22

Key: 4 I 6 I 0 = $64, $60So this is how it works, cover up the Poodle side with your hand. Look at the other stem-and-leaf plot on slide 5, don’t they look similar? You read the Chihuahua side like the other plot was read. To read the Poodle plot, cover up the Chihuahua side and imagine the “middle column” on the left side. The key is read much the same way, when you cover up the 4 and look on the other side of the equal, you see $60. When you cover up the 0 and switch the 4 and 6 with your eyes, you see 64 or $64.

Poodle3 1 07 5 58 7 6 5 48 8 5 5

Back to Back Stem & Leaf Plot

4567

Chihuahua0 0 2 3 31 1 2 3 5 50 2 22

Key: 4 I 6 I 0 = $64, $60Now we need to find the median of the prices of Poodles and the median of prices for Chihuahuas. To do this we will cross out the right and left sides of each one separately to find the middle or median.Poodle Median: 67Chihuahua Median: 53 Conclusion: In general, Poodles cost more than Chihuahuas from breeders.

Find the median, lower quartile and higher

quartile. Also find the maximum and minimum.

Box-and-Whisker Plot

20 22 27 31 46 47 54

Median: 31, the number that splits it in half.Lower Quartile: 22, the half of the smaller numbersHigher Quartile: 47, the half of the larger numbersMinimum: 20, smallest number.Maximum: 54, biggest number.Now you need to place these things on a numbered line (next slide).

Box-and-Whisker Plot

10 20 30 40 50 60 70 80 90

Box-and-Whisker Plot

minimummaximum

median

Higher Quartile Lower Quartile

It doesn’t matter that the box was floating

since there is no scale, but if there was a scale, the box would be would be flat on the line.

Mini Lesson: Box Position

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