Question

Shawn would like to know the average height of the trees in the back field at school. She measures the heights of each tree in a random sample of 20 trees. The mean height of Shawn's sample is 61 inches, and the MAD (mean absolute deviation) is 2 inches.

Answer 1

Select all that apply

Question options :

The median height of the sample must be between 59 and 63 inches.

Another random sample of 20 trees is likely to have a mean between 57 and 65 inches.

The mean height of these 20 trees is likely to be the same as the mean height of all trees in the back field .

The mean height of these 20 trees is likely to be the same as the mean height of a second random sample of 20 trees.

Shawn would be more likely to get an accurate estimate of the mean height of the population by sampling 40 trees instead of sampling 20 trees.

Answer:

The median height of the sample must be between 59 and 63 inches.

The mean height of these 20 trees is likely to be the same as the mean height of all trees in the back field .

The mean height of these 20 trees is likely to be the same as the mean height of a second random sample of 20 trees.

Shawn would be more likely to get an accurate estimate of the mean height of the population by sampling 40 trees instead of sampling 20 trees

Explanation:

The mean absolute deviation is the summary of absolute deviations from the central point or average of a data set. The central point measurement can be the mean, median or mode of the data set. An average absolute deviation can be used instead of a standard deviation to measure dispersion from central point.

In the above case, a sample is taken of 20 trees and there is a mean absolute deviation of 2, hence, median can be between 59 and 63. Also sample represents population, therefore mean of another sample taken is likely to be same as the previous one taken. Mean invariably gets more accurate as sample size increases too.