Question

name:
date: 9/12 block 3e
lesson 9: standard deviation continued
do now:
describe the difference between standard deviation and iqr.
1 the heights of the 40 trees in each of two forests are collected
mean: 44.8 feet
tree height in forest a (feet)
mean: 56.03 feet
tree height in forest b (feet)
a) which graph has a higher standard deviation?
b) what does the higher standard deviation represent in the context of the problem?
c) which forest has more consistent heights in the trees?

Explanation:

Step1: Recall definitions

Standard - deviation measures the spread of data around the mean. IQR (Inter - Quartile Range) is the difference between the third quartile and the first quartile, representing the middle 50% of the data.

Step2: Analyze dot - plots for standard deviation

For the dot - plots of tree heights in forests A and B, in forest B, the data points are more spread out from the mean (56.03 feet) compared to forest A (mean 44.8 feet). So forest B has a higher standard deviation.

Step3: Interpret higher standard deviation

A higher standard deviation in the context of tree heights means that the tree heights in forest B vary more widely from the average tree height in that forest.

Step4: Determine consistent heights

The forest with a lower standard deviation has more consistent heights. Since forest A has a lower standard deviation, forest A has more consistent tree heights.

Answer:

a) Forest B has a higher standard deviation.
b) It means the tree heights in forest B vary more widely from the average tree height in forest B.
c) Forest A has more consistent tree heights.