Question

(3.2.15) Listed below are foot lengths in inches for 11 randomly selected people taken in 1988. Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results. Are the statistics representative of the current population of all​ people?
8.6,9.2,8.8,9.3,8.5,9.9,10.2,8.9,10.2,10.5,9.7

Answer 1

The range of a set of data is the difference between the highest and lowest values in the set.

$$range=10.5-8.5=2.00in$$

The variance (σ²) is a measure of how far each value in the data set is from the mean. Here is how it is defined:

1. Subtract the mean from each value in the data. This gives you a measure of the distance of each value from the mean.
2. Square each of these distances (so that they are all positive values), and add all of the squares together.
3. Divide the sum of the squares by the number of values in the data set.

$mean=($8.6+9.2+8.8+9.3+8.5+9.9+10.2+8.9+10.2+10.5+9.7)/11=9.436in

$variance(=((8.6-0.9436)^2+(9.2-0.9436)^2+(8.8-0.9436)^2+(9.3-0.9436)^2+(8.5-0.9436)^2+(9.9-0.9436)^2+(10.2-0.9436)^2+(8.9-0.9436)^2+(10.2-0.9436)^2+(10.5-0.9436)^2+(9.7-0.9436)^2)=0.447768in^2$

The standard deviation (σ) is simply the (positive) square root of the variance.

$\sigma=\sqrt{\smash[b]{variance}}=\sqrt{\smash[b]{0.447768}}=0.6691in$

Include appropriate units in the results. Are the statistics representative of the current population of all​ people? -Yes

The statistics are representative because they are taken from the random sample.