Question

ms. hernandez asked her 14 students how many books each had read last summer. the smallest response was 7 books, and the largest was 13 books. the table gives the mean, median, range, and interquartile range (iqr) of the data set.
(a) select the best description of center for the data set.
the \average\ number of books read was about 14, which is the number of students in the class.
the \average\ number of books read was about 10, based on the mean and median.
the \average\ number of books read was about 2 to 6, based on the iqr and range.
(b) select the best description of spread for the data set.
we can tell by the range that the difference between the largest and smallest number of books read is 6.
we can tell by the median that the difference between the largest and smallest number of books read is 10.
we can tell by the number of students in the class that the difference between the largest and smallest number of books read is 14.
(c) select the graph with the shape that best fits the summary values.
graph 1 (the data set is not symmetric.)
graph 2 (the data set is symmetric.)

Explanation:

Step1: Understand measures of center

Mean and median are measures of center. Given mean = 10 and median = 10, they suggest the "average" (a general - sense of central value) number of books read is about 10.

Step2: Understand measures of spread

Range is the difference between the largest and smallest values. Given range = 6, it shows the difference between the largest and smallest number of books read is 6.

Step3: Analyze data - set shape

When mean = median, the data - set is likely to be symmetric.

Answer:

(a) The "average" number of books read was about 10, 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 6.
(c) Graph 2 (The data set is symmetric.)