Question

the table shows data for the number of customers that shopped each hour at store a and store 8 a.m. 9 a.m. 10 a.m. 11 a.m. 12 p.m. 1 p.m. 2 p.m. 3 p.m. 4 p.m. 5 p.m. store a 2 3 5 7 10 6 8 9 4 2 store b 1 4 4 6 10 8 8 6 4 2 move the options to the blanks to answer each question. which store’s data has the greater mean? which store’s data has the greater median? which store’s data has greater range?

Explanation:

Step 1: Organize Data for Store A and Store B

First, we list the number of customers for each store at each time:

• Store A: \(2, 3, 5, 7, 10, 6, 8, 9, 4, 2\)
• Store B: \(1, 4, 4, 6, 10, 8, 8, 6, 4, 2\)

We will sort these data sets to make it easier to calculate the mean, median, and range.

Step 2: Sort the Data

• Store A (sorted): \(2, 2, 3, 4, 5, 6, 7, 8, 9, 10\)
• Store B (sorted): \(1, 2, 4, 4, 4, 6, 6, 8, 8, 10\)

Step 3: Calculate the Mean

The mean is calculated by summing all the values and dividing by the number of values (n = 10 for both stores).

• Store A Mean:

Sum of values: \(2 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 56\)
Mean: \(\frac{56}{10} = 5.6\)

• Store B Mean:

Sum of values: \(1 + 2 + 4 + 4 + 4 + 6 + 6 + 8 + 8 + 10 = 53\)
Mean: \(\frac{53}{10} = 5.3\)

Since \(5.6 > 5.3\), Store A has a greater mean.

Step 4: Calculate the Median

The median is the middle value of a sorted data set. For n = 10 (even), the median is the average of the 5th and 6th values.

• Store A Median:

5th value: \(5\), 6th value: \(6\)
Median: \(\frac{5 + 6}{2} = 5.5\)

• Store B Median:

5th value: \(4\), 6th value: \(6\)
Median: \(\frac{4 + 6}{2} = 5\)

Since \(5.5 > 5\), Store A has a greater median.

Step 5: Calculate the Range

The range is the difference between the maximum and minimum values.

• Store A Range:

Maximum: \(10\), Minimum: \(2\)
Range: \(10 - 2 = 8\)

• Store B Range:

Maximum: \(10\), Minimum: \(1\)
Range: \(10 - 1 = 9\)

Since \(9 > 8\), Store B has a greater range.

Answer:

• Which store’s data has the greater mean? Store A
• Which store’s data has the greater median? Store A
• Which store’s data has the greater range? Store B