Grouped Frequency Distribution and Class Limits Statistics Problem

Published on August 25, 2026

Statistics

Learn how to organize raw data into a grouped frequency distribution table and calculate class limits, class marks, and midpoints for statistical analysis.

Question

1 number

Answer

To solve the math problem presented in the image, we will focus on the first question, which involves organizing a set of raw data into a grouped frequency distribution.

Problem Statement (Question 1)

The marks obtained by 40 students in a statistics test are given below:


50	48	47	54	32	38	71	26	67	67
52	51	55	57	38	58	22	84	27	15
66	67	33	58	62	64	10	88	94	91
40	45	56	34	28	67	85	22	96	67

Tasks:
a) Prepare a grouped frequency distribution for the above data.
b) Find the upper limit of the fourth class.
c) Find the lower limit of the third class.
d) Find the class mark (midpoint) of the sixth class.

Step-by-Step Solution

Step 1: Analyze the data

First, let’s identify the range of the data:

Minimum value:
Maximum value:
Number of observations ():
Range:

To create a grouped frequency distribution, we need to decide on the number of classes and the class width. A common approach is to use a class width of

. Let’s use a class width of

starting from

to cover the entire range.