Question

our class recorded the temperature at noon each day for 45 school days in the spring. the lowest temperature (in °f) was 68, and the highest was 76. the table gives the mean, median, range, and interquartile range (iqr) of the data set.
summary values
mean median range iqr
72 72 8 4
(a) select the best description of center for the data set.
looking at the range, we see that a \typical\ day had a temperature of about 8 °f.
looking at the mean and median, we see that a \typical\ day had a temperature of about 72 °f.
looking at the iqr, we see that a \typical\ day had a temperature of about 4 °f.
(b) select the best description of spread for the data set.
the difference between the largest and smallest temperature (in °f) is 8. (this is the range.)
the difference between the largest and smallest temperature (in °f) is 72. (this is the mean.)
the difference between the largest and smallest temperature (in °f) is 45. (this is the number of days the temperature was recorded.)
(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: Recall measures of center

The mean and median are measures of center. Given mean = 72 and median = 72, they represent the central - tendency.

Step2: Recall measure of spread

The range is the difference between the largest and smallest values. Here range = 8, which represents the spread.

Step3: Analyze data symmetry

When mean = median, the data is symmetric.

Answer:

(a) Looking at the mean and median, we see that a "typical" day had a temperature of about 72 °F.
(b) The difference between the largest and smallest temperature (in °F) is 8. (This is the range.)
(c) Graph 2 (The data set is symmetric.)