Question

Elena would like to know the average height of seventh graders in her school district. She measures the heights of everyone in a random sample of 20 students. The mean height of Elena's sample is 58 inches, and the MAD (mean absolute deviation) is 3 inches. Select all the true statements. The mean height of all seventh graders is likely be between 52 and 64 inches. Another random sample of 20 students will always have a mean of 58 inches. A sample of 20 female students would be more likely to get an accurate estimate of the mean height of the population than a sample of a mix of 20 male and female students. m A sample of 100 seventh graders would be more likely to get an accurate estimate of the mean height of the population than a sample of 20 seventh graders. a Elena's sample proves that half of all seventh graders are taller than 58 inches.​

Answer 1

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

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

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

Explanation:

The mean absolute deviation shows the variation in a given data set. It can be determined by calculating the mean of the absolute value of the initial mean and each data set. It describes how spread out the data set are.

With respect to Elena's sampling, the mean absolute deviation is 2. This shows that there is little variation among the data set.

The estimate becomes more accurate if she increase the sample size. Thus options A, B and E are appropriate.