Question

3. There are 350 people in an office building. A local deli randomly surveyed people in the building to determine the average amount spent on lunch each week. Two samples are shown.

Sample 1: {$30, $25, $10, $25, $10} and Sample 2: {$5, $60, $10, $30, $50}

(a) Calculate the mean and the median of each sample.

(b) Which sample has the least spread among its data values? Which sample has the least deviations from the mean among its values?

(c) A third sample was obtained: {$30, $25, $20, $20, $25}. Which data set in Part (a) has measures of center that align more closely with the mean and the median of the new sample? Based on the three samples, which sample is least representative of the population?

Answer 1

(a)Sample 1

The Mean = 20

The median = 25

Sample 2

The Mean = 31

The median = 60

(b) Sample 1 has the least spread

Sample 1 has the least deviations from the mean

(c) Sample 1 align with the third sample

The least representative of the population is sample 1

Explanation:

The mean is ∑fx/∑f

∑fx = 30 + 25 + 10 + 25 + 10 = 100

∑f = 5

Mean = 100/5 = 20

For the median, we arrange the data in increasing order;

10, 10, 25, 25, 30

The median = the middle number = 25

Sample 2

The mean is ∑fx/∑f

∑fx = 5 + 60 + 10 + 30 + 50 = 155

∑f = 5

Mean = 155/5 = 31

For the median, we arrange the data in increasing order;

5, 10, 30, 50, 60

The median = the middle number = 30

(b) Sample 1 range =$30 -$10 = $20

Sample 2 range =$65 -$5 = $60

Sample 1 has the least spread

Sample 1 standard deviation = 9.354

Sample 2 standard deviation =24.083

Sample 1 has the least deviations from the mean

(c) $30, $25, $20, $20, $25

Mean = 24

$20, $20, $25, $25, $30

Median = $25

∑fx = 120

Therefore sample 1 align with the third sample

The least representative of the population is sample 1 with ∑fx = 100.