Question

Use the accompanying data set to complete the following actions.

a. Find the quartiles.
b. Find the interquartile range.
c. Identify any outliers.
55 56 61 58 63 58 65 59 64 58 54 63 63 57 75

Find the quartiles.
First Q1 is _
Second Q2 is _
Third Q3 is_

Answer 1

Kindly check explanation

Explanation:

Ordered data:

54, 55, 56, 57, 58, 58, 58, 59, 61, 63, 63, 63, 64, 65, 75

Sample size, n = 15

Q1 = 1/4(n+1)th term

Q1 = 16/4 = 4th term = 57

Q2 = 1/2(n+1) th term

Q2 = 16/2 = 8th term = 59

Q3 = 3/4(n+1)th term

Q3 = 3/4(16) = 12 th term = 63

Interquartile range = Q3 - Q1 = 63 - 57 = 6

Outlier :

LOWER = Q1 - (1.5 * IQR) = 57 - (1.5*6) = 48 ; values below 48

UPPER = Q3 + (1.5 * IQR) = 63 + (1.5*6) = 72 ;

Values above 72

Outlier = 75