1. Unit 7. Day 6.

2. Describing Data
𝐽𝑜𝑟𝑑𝑎𝑛
𝐶ℎ𝑜𝑐𝑜𝑙𝑎𝑡𝑒
𝐷𝑜𝑛𝑎𝑡𝑒𝑙𝑙𝑜 A
𝑌𝑜𝑠𝑡
𝑆𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑦
𝐿𝑒𝑜𝑛𝑎𝑟𝑑𝑜 B
𝑉𝑎𝑛𝑖𝑙𝑙𝑎
𝑀𝑖𝑐ℎ𝑎𝑒𝑙𝑎𝑛𝑔𝑒𝑙𝑜 C
𝑅𝑎𝑝ℎ𝑎𝑒𝑙 D F
When there are only a few possible options, describing the data is fairly easy
(i.e. 45 students prefer chocolate, 12 prefer strawberry, and 20 prefer vanilla)

3. Test results in Mr. Jordan’s class84 74 80 92 96 84 68 72 50 84 52 44 40 76 87 82 74 90 66 52 78 84 80 88 84 76 84 58 22 54 58 58 82 72 90 78 70 88 88 69 66 58 72 60 68 86 57 68 82 54 46 56 72 61 34 48 58 74 38 64 86 87 86 67 58 63 54 86 82 74 72 76 82 75 62 88 90 50 68 75
When there are multiple options, describing the data is more difficult.
(i.e. One student earned a 22, another earned a 34, another earned a 38, …)

4. One method is to use the stem-and-leaf (remember this from 6th grade?)84 74 80 92 96 84 68 72 50 84 52 44 40 76 87 82 74 90 66 52 78 84 80 88 84 76 84 58 22 54 58 58 82 72 90 78 70 88 88 69 66 58 72 60 68 86 57 68 82 54 46 56 72 61 34 48 58 74 38 64 86 87 86 67 58 63 54 86 82 74 72 76 82 75 62 88 90 50 68 75 1 2 3 4 5 6
One method is to use the stem-and-leaf (remember this from 6th grade?) 7 8 9

5. 22, 34, 38, 40, 44, 46, 48, 50, 50, 52, 52, 54, 54, 54, 56, 57, 58, 58, 58, 58, 58, 58, 60, 61, 62, 63, 64, 66, 66, 67, 68, 68, 68, 68, 69, 70, 72, 72, 72, 72, 72, 74, 74, 74, 74, 75, 75, 76, 76, 76, 78, 78, 79, 80, 80, 82, 82, 82, 82, 82, 84, 84, 84, 84, 84, 84, 86, 86, 86, 86, 87, 87, 88, 88, 88, 88, 90, 90, 92, 96
But the older you get, the less we use stem-and-leaf. Instead we pick a “measure of center.” 1 2 2 3
4, 8 4
0, 4, 6, 8 5
0, 0, 2, 2, 4, 4, 4, 6, 7, 8, 8, 8, 8, 8, 8, 8 6
0, 1, 2, 3, 4, 6, 6, 7, 8, 8, 8, 8, 9 7
0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 5, 5, 6, 6, 6, 8, 8, 9 8
0, 0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8 9
0, 0, 2, 2, 6

6. Mean, Median, & Mode Test results in Mr. Jordan’s class84 74 80 92 96 84 68 72 50 84 52 44 40 76 87 82 74 90 66 52 78 84 80 88 84 76 84 58 22 54 58 58 82 72 90 78 70 88 88 69 66 58 72 60 68 86 57 68 82 54 46 56 72 61 34 48 58 74 38 64 86 87 86 67 58 54 82 74 72 76 82 75 62 63 86 88 90 50 68 75
I want to describe the overall outcome on the test.
I want a value that will give me a general picture.
I want a value that measures the “central location”.
There are three ways to measure this “central tendency”

7. Mean: arithmetic average
Median: Middle
Mode: Popular

8. This is something you learned in 6th grade
Example A*: Find the mean, median, and mode for the quiz scores.
This is something you learned in 6th grade
7, 2, 9, 2, 8, 6, 6, 2, 10, 2, 10, 8 7 2 9 2 8 6 6 2 10 2 10 8
Mean: 7 + 2 + 9 + 2 + 8 + 6 + 6 + 2 + 10 + 2 + 10 + 8 6
72 12 6 = 12
CCSS.MATH.CONTENT.6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number …
13 2
Median:
6.5
6 1 2
Mean
Median
Mode
Mode: 2

9. Are you ready for a 7th grade problem?

10. 101 69 6969 101 Example B: Find the mean, median, and mode. Mean87 76 29 85 72 58 48 69 70 75 77 81 66 92 86 79 71 65 54 73 80 89 74
100 68 39 50 84 90 8 99 52 28 82 62 57 88 32 78 83 33 49 95 60 30 55 31 44 98 40 42 96 46 63 56 67 91
CCSS.MATH.CONTENT.7.SP.A.1 Understand that:
statistics can be used to gain information about a population by examining a sample of the population;
generalizations about a population from a sample are valid only if the sample is representative of that population.
random sampling tends to produce representative samples and support valid inferences.
Mean 87 + 76 + 29 + 85 + 72 + … + 89
101 69

11. 10 67.6 676 10 Example B: Find the mean, median, and mode. Mean 69 +87 76 29 85 72 58 48 69 70 75 77 81 66 92 86 79 71 65 54 73 80 89 74
100 68 39 50 84 90 8 99 52 28 82 62 57 88 32 78 83 33 49 95 60 30 55 31 44 98 40 42 96 46 63 56 67 91
Mean 69 + 85 + 29 + 70 + 87 + 39 + 83 + 80 + 44 + 90 10
676 10
67.6

12. Example B: Find the mean, median, and mode.87 76 29 85 72 58 48 69 70 75 77 81 66 92 86 79 71 65 54 73 80 89 74
100 68 39 50 84 90 8 99 52 28 82 62 57 88 32 78 83 33 49 95 60 30 55 31 44 98 40 42 96 46 63 56 67 91
Median 8 40 42 44 46 28 29 30 31 32 33 39
If you took the time … the median would be: 74

13. Example B: Find the mean, median, and mode.87 76 29 85 72 58 48 69 70 75 77 81 66 92 86 79 71 65 54 73 80 89 74
100 68 39 50 84 90 8 99 52 28 82 62 57 88 32 78 83 33 49 95 60 30 55 31 44 98 40 42 96 46 63 56 67 91
Median 29 39 44 69 70 80 83 85 87 90
150 2 = = 75

14. N/A 77 Example B: Find the mean, median, and mode. Mode 87 76 29 85 7258 48 69 70 75 77 81 66 92 86 79 71 65 54 73 80 89 74
100 68 39 50 84 90 8 99 52 28 82 62 57 88 32 78 83 33 49 95 60 30 55 31 44 98 40 42 96 46 63 56 67 91
Mode 77
N/A

15. 69 67.6 74 75 - 77 Example B: Find the mean, median, and mode.87 76 29 85 72 58 48 69 70 75 77 81 66 92 86 79 71 65 54 73 80 89 74
100 68 39 50 84 90 8 99 52 28 82 62 57 88 32 78 83 33 49 95 60 30 55 31 44 98 40 42 96 46 63 56 67 91
Now you will take your own random sample and see how close your sample measures of center are to the population measures of center.
Population (all #s)
Sample
MEAN
MEDIAN
MODE 69
67.6 74 75 - 77