The mean is 15.9, median is 16 and interquartile is 14.5
Explanation:
The given data set is 27,16,8,5,19,14,22,31,13,5,23,16,8.
To find Mean :
Mean = Sum of all the elements in the data / Total number of elements.
Mean = (27+16+8+5+19+14+22+31+13+5+23+16+8) / 13
Mean = 207 / 13
Mean = 15.9
To find Median :
The median is the middle term after arranging the data set in an ascending order.
Step 1 :
Arrange data set in ascending order
⇒ 5,5,8,8,13,14,16,16,19,22,23,27,31
Step 2 :
choose the middle term from the rearranged order.
⇒ middle term = n+1 / 2
where n is the total number of elements in the set.
⇒ middle term = 13+1 / 2 = 7th term
⇒ 7th term = 16
Median = 16
To find the interquartile :
Interquartile = Q3 - Q1
where, Q3 is the third quartile and Q1 is the first quartile.
Step 1 :
Arrange data set in ascending order
⇒ 5,5,8,8,13,14,16,16,19,22,23,27,31
Step 2 :
Find the median. The median is 16.
Step 3 :
Find Q1. It is the median of the elements in the first half of elements in the data set.
⇒ (5,5,8,8,13,14)
⇒ median is the average of two middle terms.
⇒ Q1 = (8+8)/2 = 16/2
⇒ Q1 = 8
Step 4 :
Find Q3. It is the median of the elements in the second half of elements in the data set.
⇒ (16,19,22,23,27,31)
⇒ median is the average of two middle terms.
⇒ Q3 = (22+23)/2 = 45/2
⇒ Q3 = 22.5
Step 5 :
Interquartile = 22.5 - 8
Interquartile = 14.5