Question

The stem-and-leaf plot shows the heights in centimeters of Teddy Bear sunflowers grown in two different types of soil.

Soil A Soil B

5 9

5 2 1 1 6 3 9

5 1 0 7 0 2 3 6 7 8

2 1 8 3

0 9

Key: 9|6 means 69 Key: 5|8 means 58

Calculate the mean of each data set.

Calculate the mean absolute deviation (MAD) of each data set.

Which set is more variable? How do you know?

Answer 1

Soil A mean: 71.8

Soil B mean: 72

Soil A MAD: 8.16

Soil B MAD: 5.4

Soil A set is more variable because it has a greater MAD. This feature is also seen in the stem-and-leaf plot, where Soil A set is more spread than Soil B set

Explanation:

Soil A | |Soil B

|5|9

5 2 1 1|6|3 9

5 1 0|7|0 2 3 6 7 8

2 1|8|3

0|9|

Soil A mean: (65 + 62 + 61 + 61 + 75 + 71 + 70 + 82 + 81 + 90)/10 = 71.8

Soil B mean: (59 + 63 + 69 + 70 + 72 + 73 + 76 + 77 + 78 + 83)/10 = 72

Soil A MAD: ( |65 - 71.8| + |62 - 71.8| + |61 - 71.8| + |61 - 71.8| + |75 - 71.8| + |71 - 71.8| + |70 - 71.8| + |82 - 71.8| + |81 - 71.8| + |90 - 71.8|)/10 = 8.16

Soil B MAD: ( |59-72| + |63-72| + |69-72| + |70-72| + |72-72| + |73-72| + |76-72| + |77-72| + |78-72| + |83-72| )/10 = 5.4