Question

choosing representative samples
linda randomly surveyed 20 teachers at her school about whether they prefer chalkboards or dry erase boards. she repeated the survey three times with three different sets of teachers.

	chalk	dry erase
sample 2	9	11
sample 3	1	19

which pair of linda’s samples seems to have the lowest variability and, therefore, are representative samples?

• samples 1 and 2
• samples 1 and 3
• samples 2 and 3
• none of the samples

Explanation:

Step1: Calculate difference for each sample

Sample 1: $|12 - 8| = 4$
Sample 2: $|9 - 11| = 2$
Sample 3: $|1 - 19| = 18$

Step2: Compare pairwise variability

Samples 1&2: max(4,2)=4; Samples1&3: max(4,18)=18; Samples2&3: max(2,18)=18

Step3: Identify pair with lowest variability

The pair with the smallest maximum difference is Samples 1 and 2.

Answer:

samples 1 and 2