Question

1. the number of hours worked by employees in a week are 10, 15, 20, 25, 40. the sample standard deviation is 11.51. what type of variability does this data set have?

a. low variability
b. high variability
c. no variability
d. moderate variability

Explanation:

To determine the variability, we analyze the data and standard deviation. First, find the mean of the data set (10, 15, 20, 25, 40). The mean $\bar{x}=\frac{10 + 15+20 + 25+40}{5}=\frac{110}{5} = 22$. The sample standard deviation is 11.51. To assess variability, we can look at the range (40 - 10 = 30) and compare the standard deviation to the mean. The coefficient of variation (CV) is $\frac{s}{\bar{x}}\times100=\frac{11.51}{22}\times100\approx52.32\%$. A moderate variability is often associated with a CV that's not extremely low (low variability, CV << 10%) or extremely high (high variability, CV >> 100%). Here, the data has values spread but not extremely (e.g., 40 is an outlier? No, the sequence is 10,15,20,25,40 – increasing, with 40 being a larger jump from 25, but the standard deviation and CV suggest moderate. Also, "moderate" is typical for data with some spread but not extreme. Options: "No variability" is wrong (data differs). "Low" would have small spread (e.g., all near mean), "High" would have very large spread (e.g., data from 0 to 100 with big SD). So moderate fits.

Answer:

d. Moderate variability