Find the mean, median, and interquartile for the data set below. Round your answer to the nearest tenth.
27,16,8,5,19,14,22,31,13,5,23,16,8

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

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