Question

ms. hall asked her 30 students how many books each had read last summer. the smallest response was 10 books, and the largest was 17 books. the table gives the mean, median, range, and interquartile range (iqr) of the data set.
summary values
mean 13.5
median 13.5
range 7
iqr 1
(a) select the best description of center for the data set.
the \average\ number of books read was about 30, which is the number of students in the class.
the \average\ number of books read was about 13 or 14, based on the mean and median.
the \average\ number of books read was about 1 to 7, based on the iqr and range.
(b) select the best description of spread for the data set.
we can tell by the number of students in the class that the difference between the largest and smallest number of books read is 30.
we can tell by the median that the difference between the largest and smallest number of books read is 13.5.
we can tell by the range that the difference between the largest and smallest number of books read is 7.
(c) select the graph with the shape that best fits the summary values.
graph 1 (the data set is symmetric.)
graph 2 (the data set is not symmetric.)

Explanation:

Step1: Recall definitions of central - tendency and spread

The mean and median are measures of center. The range and inter - quartile range (IQR) are measures of spread.

Step2: Analyze part (a)

The "average" usually refers to the mean. Given mean = 13.5 and median = 13.5, the best description of the center is that the "average" number of books read was about 13 or 14, based on the mean and median.

Step3: Analyze part (b)

The range is calculated as the largest value minus the smallest value. Given largest = 17 and smallest = 10, range=17 - 10=7. The IQR is given as 1. The best description of spread is that we can tell by the range that the difference between the largest and smallest number of books read is 7.

Step4: Analyze part (c)

Since the mean and median are close (13.5 and 13.5), and looking at the shape of the data distribution from the histograms, a symmetric distribution is one where the mean and median are approximately equal. Graph 1 has a more symmetric shape.

Answer:

(a) The "average" number of books read was about 13 or 14, based on the mean and median.
(b) We can tell by the range that the difference between the largest and smallest number of books read is 7.
(c) Graph 1 (The data set is symmetric.)