Question

Use the accompanying data set to complete the following actions.

a. Find the quartiles.

b. Find the interquartile range.

c. Identify any outliers.

57, 58, 60, 63, 63, 58, 59, 62, 62, 63, 61, 59, 58, 54, 77

The first quartile, Q1,

The first quartile, Q1,

The second quartile, Q2,

The third quartile, Q 3,

(Type integers or decimals.)

b. Find the interquartile range.

The interquartile range (IQR) is

c. Identify any outliers.

Choose the correct answer below.

A. There exists at least one outlier in the data set at

(Use a comma to separate answers as needed.)

B. There are no outliers in the data set.

Step 1

Given data points

57, 58, 60, 63, 63, 58, 59, 62, 62, 63, 61, 59, 58, 54, 77

We need to find quartile1 quartile 3.

First step is to arrange data in ascending order

54, 57,58,58,58,59,59,60,61,62,62,63,63,63,77

The median is the mid point in these 15 data points which is the 8th data point = 60

Quartile 1 is the middle point between lowest data 54 point and median 60. There are total 8 data points 54 to 60, so their median is average of 4th and 5th data points which are both 58. So Quartile 1 = (58+58)/2 = 58.

Quartile 3 is the middle point between median 60 and maximum data point 77. There are total 8 data points from 60 to 77, so their median is average of 4th and 5th data points which are 62,63 . So Quartile 3 = (62+63)/2 = 62.5.

So we can say Quartile 1 = 58, Quartile 2 = median = 60, Quartile 3 = 62.5

Step 2

Inter quartile range = Quartile 3 - ...

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