Question

What are the lower, middle, and upper quartiles of this data? 122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Answer 1

Answer:

The lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.

Step-by-step explanation:

The given data set is

122, 164, 71, 98, 84, 147, 114, 111, 98, 85, 104, 71, 77

Arrange the data set in ascending order.

71, 71, 77, 84, 85, 98, 98, 104, 111, 114, 122, 147, 164

Divide the data set in equal parts.

(71, 71, 77, 84, 85, 98), 98, (104, 111, 114, 122, 147, 164)

Now divide each parenthesis in two equal parts.

(71, 71, 77), (84, 85, 98), 98, (104, 111, 114), (122, 147, 164)

Lower quartile is

$Q_1=\frac{77+84}{2}=80.5$

Middle quartile is

$Median=Q_2=98$

Upper quartile is

$Q_3=\frac{114+122}{2}=118$

Therefore, the lower, middle, and upper quartiles of this data are 80.5, 98 and 118 respectively.