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 72 median 72 range 8 iqr 4 (a) select the best description of spread for the data set. 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.) the difference between the largest and smallest temperature (in °f) is 8. (this is the range.) (b) select the best description of center for the data set. looking at the mean and median, we see that a \typical\ day had a temperature of about 72 °f. looking at the range, we see that a \typical\ day had a temperature of about 8 °f. looking at the iqr, we see that a \typical\ day had a temperature of about 4 °f. (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 definitions

The range is the difference between the largest and smallest values in a data - set. Here, the lowest temperature is 68°F and the highest is 76°F, so the range is 76 - 68=8°F. The inter - quartile range (IQR) is the difference between the third quartile and the first quartile. Given that the IQR is 4°F.

Step2: Analyze part (a)

The spread of a data - set can be described by the range. The difference between the largest and smallest temperature values gives the range of the data set. Here, the range is 8°F, so the best description for the spread is "The difference between the largest and smallest temperature (in °F) is 8. (This is the range.)"

Step3: Analyze part (b)

The center of a data set can be described by the mean or median. Given that the mean and median are both 72°F, looking at the mean and median, we see that a "typical" day had a temperature of about 72°F.

Step4: Analyze part (c)

The data set with a range of 8°F and IQR of 4°F and non - symmetric distribution (since the spread and other characteristics suggest non - symmetry) is best represented by Graph 1 as it is non - symmetric.

Answer:

(a) The difference between the largest and smallest temperature (in °F) is 8. (This is the range.)
(b) Looking at the mean and median, we see that a "typical" day had a temperature of about 72°F.
(c) Graph 1 (The data set is not symmetric.)