Question

The stem and leaf plot shows the height in centimeters of teddy bears and flowers 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
a) calculate the mean of each data set
b) calculate the mean, absolute deviation of each data set
c) which state is more variable? How do you know?

Answer 1

Ty bot













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Answer 2

Let's first list down the data from the stem and leaf plot.
Soil A: 52, 51, 51, 51, 50, 21, 20, 0
Soil B: 59, 63, 69, 70, 72, 73, 76, 77, 78, 83

a) To calculate the mean of each data set, add the numbers and divide by the number of data points.
Soil A mean = (52+51+51+51+50+21+20+0) / 8 = 296 / 8 = 37 cm
Soil B mean = (59+63+69+70+72+73+76+77+78+83) / 10 = 720 / 10 = 72 cm

b) The mean absolute deviation (MAD) is calculated as the average of the absolute differences between each data point and the mean. First, find the absolute differences for each data point, then average them.

Soil A absolute differences: |52-37|=15, |51-37|=14, |51-37|=14, |51-37|=14, |50-37|=13, |21-37|=16, |20-37|=17, |0-37|=37
Mean absolute deviation for Soil A = (15+14+14+14+13+16+17+37) / 8 = 140 / 8 = 17.5 cm

Soil B absolute differences: |59-72|=13, |63-72|=9, |69-72|=3, |70-72|=2, |72-72|=0, |73-72|=1, |76-72|=4, |77-72|=5, |78-72|=6, |83-72|=11
Mean absolute deviation for Soil B = (13+9+3+2+0+1+4+5+6+11) / 10 = 54 / 10 = 5.4 cm

c) The more variable data set is the one with the higher mean absolute deviation. In this case, Soil A is more variable, because its MAD (17.5 cm) is higher than Soil B's MAD (5.4 cm). This means that the height of the teddy bears and flowers grown in Soil A varies more from the mean height compared to those grown in Soil B.

Answer 3

You're welcome! 🐾