Question

question 12 of 25
what are the more appropriate measures of center and
spread for this data set?

select two choices: one for the center and one for the spread.

a. better measure of spread: standard deviation

b. better measure of center: mean

c. better measure of center: median

d. better measure of spread: interquartile range (iqr)

Explanation:

Step1: Analyze the data set (box - plot)

The box - plot shows that there is an outlier (the data point at 26) or the data is skewed. When data is skewed or has outliers, the median is a better measure of center than the mean because the mean is affected by extreme values.

Step2: Analyze measures of spread

For skewed data or data with outliers, the interquartile range (IQR) is a better measure of spread than the standard deviation. The standard deviation is also affected by extreme values, while the IQR measures the spread of the middle 50% of the data and is resistant to outliers.

Step3: Evaluate the options

• Option A: Standard deviation is not a good measure of spread for skewed data with outliers, so A is incorrect.
• Option B: Mean is affected by the outlier (26), so median is better. Thus, B is incorrect.
• Option C: Median is a good measure of center for skewed data with outliers, so C is correct.
• Option D: IQR is a good measure of spread for skewed data with outliers, so D is correct.

Answer:

C. Better measure of center: median
D. Better measure of spread: interquartile range (IQR)