Question

Question 1: Descriptive Statistics: Each question is worth 2 marks: Total Data: 22 24 26 26 28 30 32 38 44 A. What is the mean? B. What is the median? C. What is the mode? D. What is the 25th and 75th percentile? E. What is the interquartile range?

Answer 1

Solution:- Given that samples : 22,24,26,26,28,30,32,38,44

A. mean = sum of the terms/ number of terms

= (22 + 24 + 26 + 26 + 28 + 30 + 32 + 38 + 44)/9

= 270/9

= 30

B. Median = 28

Explanation

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

22 24 26 26 28 30 32 38 44   

So, the median is 28 .

C. Mode = 26

Explanation

The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

22 24 26 26 28 30 32 38 44   

We see that the mode is 26 .

D. => 25th percentile = 26

The percentile is at the position i = 3 it is 26

=> 75th percentile = 32

The percentile is at the position i = 7 it is 32

E. Interquartile Range (IQR) = 10

Explanation :

The interquartile range is the difference between the third and first quartiles.

The third quartile is 35.

The first quartile is 25.

The interquartile range = 35 - 25 = 10.