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 52
median 51
range 7
iqr 4
(a) select the best description of spread for the data set.
the middle half of the data set is 4 units wide. (this is the iqr.)
the middle half of the data set is 51 units wide. (this is the median.)
the middle half of the data set is 31 units wide. (this is the number of tours given.)
(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 not symmetric.)
graph 2 (the data set is symmetric.)

Explanation:

Step1: Analyze spread description

The inter - quartile range (IQR) represents the middle half of the data set. Given IQR = 4, the best description of the spread for the data set is that the middle half of the data set is 4 units wide. So for part (a), the answer is "The middle half of the data set is 4 units wide. (This is the IQR.)".

Step2: Analyze center description

The median and mean are measures of the center of a data - set. Given median = 51 and mean = 52, based on the median and mean, we see that the "average" number of people served was about 51 or 52. So for part (b), the answer is "Based on the median and mean, we see that the 'average' number of people served was about 51 or 52."

Step3: Analyze graph shape

The summary values are: mean = 52, median = 51, range = 7, IQR = 4. Since the mean is slightly larger than the median and the data set is not symmetric, Graph 1 which is not symmetric best fits the summary values. So for part (c), the answer is "Graph 1 (The data set is not symmetric.)"

Answer:

(a) The middle half of the data set is 4 units wide. (This is the IQR.)
(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 not symmetric.)