393,770 views
8 votes
8 votes
Here are yesterday's high temperatures (in Fahrenheit) in 13 U.S. cities.

50, 51, 55, 55, 59, 59, 64, 67, 67, 74, 77, 78, 80
Notice that the temperatures are ordered from least to greatest.
Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:

User Play
by
3.0k points

1 Answer

19 votes
19 votes

Answer:

To find the five-number summary for a set of data, we need to find the minimum, first quartile, median, third quartile, and maximum of the data. To find the interquartile range, we subtract the first quartile from the third quartile.

The minimum temperature in the list is 50 degrees Fahrenheit. The maximum temperature is 80 degrees Fahrenheit. To find the median, we need to first find the middle value in the list. Since there are 13 temperatures in the list, the middle value is the seventh temperature, which is 64 degrees Fahrenheit.

To find the first and third quartiles, we need to divide the list into two halves at the median. The first half of the list contains the first six temperatures, and the second half contains the last six temperatures. The median of the first half of the list is the average of the third and fourth temperatures, which is 55 degrees Fahrenheit. The median of the second half of the list is the average of the sixth and seventh temperatures, which is 61.5 degrees Fahrenheit.

Therefore, the five-number summary for this data set is:

Minimum: 50

Lower quartile: 55

Median: 64

Upper quartile: 61.5

Maximum: 80

The interquartile range is the difference between the upper and lower quartiles, which is 61.5 - 55 = 6.5.

User Cmd
by
3.0k points