Question

Would the outlier be 43.5 or 54? And same for would it 78 or 88.5? PART C

Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 62 65 57 64 57 54 64 62 65 57 58 57 59 56 78 O The first quartile, Qy, is 57|. The second quartile, Q2, is 59 The third quartile, Q3, is 64. (Type integers or decimals.) b. Find the interquartile range. The interquartile range (IQR) is 7). (Type an integer or a decimal.) 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.

Answer 1

Sol)

Given data

62,65,57,64,57,54,64,62,65,57,58,57,59,56,78

Arranging in ascending order

55,56,57,57,57,57,58,59,62,62,64,64,65,65,78

n = 15

Median ( second quartile )

= ( n + 1 ) / 2 th term

= ( 15+1 ) / 2 th term

= 8th term

= 59

First quartile

Data before median

55,56,57,57,57,57,58

n = 7

First quartile = ( n + 1 ) / 2 th term

Q1 = ( 7 + 1 ) / 2 th term

Q1 = 4th term

= 57

Third quartile

Data after median

62,62,64,64,65,65,78

n = 7

Q3 = ( 7 + 1 ) / 2 th term

= 4th term

= 64

First quartile = 57

Second quartile = 59

Third quartile = 64

b )

Interquartile range

IQR = Q3 - Q1

= 64 - 57

= 7

Outliers

Q1 - 1.5 ( IQR )

57 - 1.5 ( 7 )

57 - 10.5

= 46.5

Q3 + 1.5 ( IQR )

64 + 1.5 ( 7 )

64 + 10.5

= 74.5

The values less than 46.5 and greater than 74.5 are considered as outliers

78 is the only value greater than 74.5

Option A

There exists at least one outlier in the data set is 78