Answer
Minimum = 61
Lower quartile = 67
Median = 72
Upper quartile = 87
Maximum = 95
Interquartile range = 20
Step-by-step explanation
61, 66, 67, 67, 69, 70, 72, 74, 82, 85, 89, 92, 95
Minimum
This is the least number in the distribution.
So,
Minimum = 61
Lower quartile
The lower quartile is given as the variable in the position of
¼ (N + 1)
N = 13
¼ (N + 1) = ¼ (13 + 1) = ¼ (14) = 3.5
The lower quartile is in between the 3rd and 4th
3rd variable = 67
4th variable = 67
Lower quartile = (67 + 67)/2 = (134/2) = 67
Median
The median is the number in the middle of the distribution when the variables are arranged in increasing or decreasing order.
For this distribution,
Median = 7th variable = 72
Upper quartile
The upper quartile is given as the variable in the position of
(3/4) (N + 1)
N = 13
(3/4) (N + 1) = (3/4) (13 + 1) = (3/4) (14) = 10.5
The upper quartile is in between the 10th and 11th variables
Upper quartile = (85 + 89)/2 = (174/2) = 87
Maximum
This is the number with the greatest value in the distribution.
Maximum = 95
Interquartile range
This is the difference between the upper and lower quartiles.
Interquartile range = (Upper quartile) - (Lower quartile)
Interquartile range = 87 - 67
Interquartile range = 20
Hope this Helps!!!