Answer
- Mean = 21.25 years.
- Minimum = 5 years.
- Range = 45 years.
- Median = 16.5 years.
- Lower quartile(Q1) = 10.5 years.
- Upper quartile(Q3) = 31 years.
Step-by-step explanation
Given the data for the average life span (in years) of 16 different animals found in Africa.
5, 10, 10, 10, 11, 14, 15, 15, 18, 20, 20, 27, 35, 40, 40, 50
We are then asked to compute some statistical quantities,
- Mean
The mean is the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
N = number of variables = 16
Σx = 5 + 10 + 10 + 10 + 11 + 14 + 15 + 15 + 18 + 20 + 20 + 27 + 35 + 40 + 40 + 50 = 340
Mean = (340/16) = 21.25 years.
- Minimum:
The minimum refers to the smallest number in the dataset.
Minimum = 5 years.
- Range
This refers to the difference between the largest number and smallest number.
Range = (Largest number) - (Smallest number)
Largest number = 50
Smallest number = 5
Range = 50 - 5 = 45 years.
- Median
The median is the number at the middle when the variables are arranged in ascending or decreasing order. It is given as the [(N+1)/2]th number.
N = number of variables = 16
(N+1)/2 = (16+1)/2 = (17/2) = 8.5th number
The numbers in ascending order is
5, 10, 10, 10, 11, 14, 15, 15, 18, 20, 20, 27, 35, 40, 40, 50
The 8.5th number will be between the 8th and the 9th number.
8th number = 15
9th number = 18
Median = (15+18)/2 = (33/2) = 16.5 years.
- Lower quartile(Q1)
The lower quartile is the number that is one quarter of the way along the ascending order of the list of the variables.
That is, the lower quartile is the [(N+1)/4]th number
N = number of variables = 16
(N+1)/4 = (16+1)/4 = (17/4) = 4.25th number
The numbers in ascending order is
5, 10, 10, 10, 11, 14, 15, 15, 18, 20, 20, 27, 35, 40, 40, 50
This number will be between the 4th number and the 5th number.
4th number = 10
5th number = 11
Lower quartile = (10+11)/2 = (21/2) = 10.5 years.
- Upper quartile(Q3)
The upper quartile is the number that is three quarter of the way along the ascending order of the list of the variables.
That is, the upper quartile is the [3(N+1)/4]th number
N = number of variables = 16
3(N+1)/4 = 3(16+1)/4 = (51/4) = 12.75th number
The numbers in ascending order is
5, 10, 10, 10, 11, 14, 15, 15, 18, 20, 20, 27, 35, 40, 40, 50
This number will be between the 12th number and the 13th number.
12th number = 27
13th number = 35
Upper quartile = (27+35)/2 = (62/2) = 31 years.
Hope this Helps!!!