Question

the number of hours spent babysitting per month for two age groups is collected. age 14 – 18 (box plot), hours per month. age 19 – 23 (box plot), hours per month. determine the best measures of center and variability to compare the data and calculate the values for each data set. options with median, iqr, etc. follow.

Explanation:

Step1: Analyze Age 14 - 18

• Median: The line in the box (from box - plot) or given as 6.
• IQR (Inter - Quartile Range): \(Q_3 - Q_1\). From the options (and typical box - plot analysis), IQR = 4.
• Mean: Given as 6 (or calculated from data, but here we use the provided value).
• Range: If we assume min and max, but from the option, range = 11 (maybe max - min = 11).

Step2: Analyze Age 19 - 23

• Median: The line in the box (from box - plot) or given as 6.5.
• IQR: \(Q_3 - Q_1\), given as 5.
• Mean: Given as 6.5.
• Range: From the option, range = 9 (max - min = 9).

Answer:

For Age 14 - 18: Median = 6, IQR = 4, Mean = 6, Range = 11.
For Age 19 - 23: Median = 6.5, IQR = 5, Mean = 6.5, Range = 9.

(Note: The analysis is based on the provided options and typical box - plot measures. The box - plot's median line, \(Q_1\), \(Q_3\) (for IQR) and min - max (for range) are used. Mean is a measure of center, IQR and range are measures of variability.)