Question

ms. tanaka asked her 32 students how many books each had read last summer. the smallest response was 10 books, and the largest was 19 books. the table gives the mean, median, range, and inter - quartile range (iqr) of the data set. (a) select the best description of center for the data set. we see that a “typical” student read about 32 books by looking at the number of students in the class. we see that a “typical” student read about 4 to 9 books by looking at the iqr and range. we see that a “typical” student read about 14 or 15 books by looking at the mean and median. (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 32. we can tell by the range that the difference between the largest and smallest number of books read is 9. we can tell by the median that the difference between the largest and smallest number of books read is 14.5. (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.) summary values mean 14.5 median 14.5 range 9 iqr 4

Explanation:

Step1: Identify center - measure

The mean is 14.5 and median is 14.5. These are measures of center. A "typical" value for center can be determined by mean and median. So, for center, we see that a "typical" student read about 14 or 15 books by looking at the mean and median.

Step2: Identify spread - measure

The range is the difference between the largest and smallest values. Here, largest is 19 and smallest is 10, so range = 19 - 10=9. So, we can tell by the range that the difference between the largest and smallest number of books read is 9.

Step3: Identify graph - shape

Since mean = median = 14.5, the data set is symmetric. Graph 1 represents a symmetric data - set.

Answer:

(a) We see that a "typical" student read about 14 or 15 books by looking at the mean and median.
(b) We can tell by the range that the difference between the largest and smallest number of books read is 9.
(c) Graph 1 (The data set is symmetric.)