Question

the number of hours worked by each of the employees last week at two stores are listed below. hours worked in a week at two stores store 1: 16, 28, 36, 40, 78 store 2: 22, 27, 33, 36, 40 which statements are true and supported by the data in the table? check all that apply. the data for store 1 shows greater variability. the median number of hours worked for the two stores is the same. the mean of the data for store 1 is greater than the mean of the data for store 2. the interquartile range of both data sets is the same. the range of the data for store 1 is less than the range of the data for store 2.

Explanation:

Step1: Calculate range for store 1

Range = Max - Min. For store 1, data is 16, 28, 36, 40, 78. Range1 = 78 - 16=62.

Step2: Calculate range for store 2

For store 2, data is 22, 27, 33, 36, 40. Range2 = 40 - 22 = 18. Since 62>18, range of store 1 is greater than store 2.

Step3: Calculate inter - quartile range (IQR)

First, find median (Q2). For store 1 (n = 5), median is the 3rd value, Q2_1=36. For lower half (16, 28), Q1_1 = 22. For upper half (40, 78), Q3_1=59. IQR1=Q3_1 - Q1_1=59 - 22 = 37. For store 2 (n = 5), median is 33. For lower half (22, 27), Q1_2 = 24.5. For upper half (36, 40), Q3_2=38. IQR2=Q3_2 - Q1_2=38 - 24.5 = 13.5. IQRs are not the same.

Step4: Calculate mean for store 1

Mean1=$\frac{16 + 28+36+40+78}{5}=\frac{198}{5}=39.6$.

Step5: Calculate mean for store 2

Mean2=$\frac{22 + 27+33+36+40}{5}=\frac{158}{5}=31.6$. Mean of store 1 is greater than store 2.

Step6: Check median

Median of store 1 is 36 and median of store 2 is 33, they are not the same.

Step7: Check variability

Range and IQR of store 1 are larger, so store 1 has greater variability.

Answer:

• The mean of the data for store 1 is greater than the mean of the data for store 2.
• The data for store 1 shows greater variability.