Question

gadabout tour company gave bus tours last summer. the tour director noted the number of people served by each of the 31 tours. the smallest number of people served was 50, and the largest was 57. the table gives the mean, median, range, and interquartile range (iqr) of the data set.
summary values
mean median range iqr
52 51 7 4
(a) select the best description of spread for the data set.
the difference between the largest and smallest number of people served is 7. (this is the range.)
the difference between the largest and smallest number of people served is 31. (this is the number of tours given.)
the difference between the largest and smallest number of people served is 52. (this is the mean.)
(b) select the best description of center for the data set.
based on the iqr, we see that the \average\ number of people served was about 4.
based on the range, we see that the \average\ number of people served was about 7.
based on the median and mean, we see that the \average\ number of people served was about 51 or 52.
(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 spread - definition

The spread of a data - set is measured by the difference between the largest and the smallest values, which is the range. Here, the range is 7, so the spread is described by the difference between the largest and smallest number of people served is 7.

Step2: Recall center - definition

The center of a data - set can be described by the mean or the median. The mean is 52 and the median is 51, so based on the median and mean, the "average" number of people served was about 51 or 52.

Step3: Analyze shape

When the mean and median are close (51 and 52), the data set is likely to be symmetric. Graph 1 represents a symmetric data set.

Answer:

(a) The difference between the largest and smallest number of people served is 7. (This is the range.)
(b) Based on the median and mean, we see that the "average" number of people served was about 51 or 52.
(c) Graph 1 (The data set is symmetric.)