Question

Find the mean, median, and interquartile for the data set below. Round your answer to the nearest tenth.

Answer 1

The mean is 15.9, median is 16 and interquartile is 14.5

Step-by-step 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