Calculating Frequency Distribution: Relative Frequency, Class Mark, and Cumulative Frequency

Math Problem Statement

For the following Frequency Distribution table, calculate: i. Relative Frequency, ii. Class Mark, iii. Width of Class Interval, iv. Cumulative Frequency Distribution.

Solution

Let's solve the given frequency distribution table by calculating the following:

1. Relative Frequency

Relative frequency is calculated as the frequency of each class divided by the total number of students.

2. Class Mark

Class mark (midpoint) is calculated as the average of the lower and upper boundaries of each class interval.

3. Width of Class Interval

The width of the class interval is the difference between the upper and lower boundaries of a class interval.

4. Cumulative Frequency Distribution

Cumulative frequency is calculated by adding the frequency of each class to the sum of the frequencies of all preceding classes.

Now, let's calculate each one:

Given Data:

Marks: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70
Number of Students: 4, 6, 10, 18, 12, 10

Total Number of Students:

$4 + 6 + 10 + 18 + 12 + 10 = 60$

Calculations:

Marks	Frequency	Relative Frequency	Class Mark	Width of Interval	Cumulative Frequency
10-20	4	$\frac{4}{60} = 0.0667$	$\frac{10+20}{2} = 15$	$20 - 10 = 10$	4
20-30	6	$\frac{6}{60} = 0.1$	$\frac{20+30}{2} = 25$	$30 - 20 = 10$	4 + 6 = 10
30-40	10	$\frac{10}{60} = 0.1667$	$\frac{30+40}{2} = 35$	$40 - 30 = 10$	10 + 10 = 20
40-50	18	$\frac{18}{60} = 0.3$	$\frac{40+50}{2} = 45$	$50 - 40 = 10$	20 + 18 = 38
50-60	12	$\frac{12}{60} = 0.2$	$\frac{50+60}{2} = 55$	$60 - 50 = 10$	38 + 12 = 50
60-70	10	$\frac{10}{60} = 0.1667$	$\frac{60+70}{2} = 65$	$70 - 60 = 10$	50 + 10 = 60

Let me know if you need further explanations or have any questions.

Questions to Explore:

How would you calculate the mean of the distribution?
What is the importance of relative frequency in data analysis?
How can you use cumulative frequency to find the median class?
Can you explain the significance of class width in data interpretation?
How would you graphically represent this data?

Tip:

When working with frequency distributions, always double-check that your cumulative frequency adds up to the total number of observations to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Relative Frequency
Class Mark
Cumulative Frequency

Formulas

Relative Frequency = (Frequency of Class) / (Total Frequency)
Class Mark = (Lower Limit + Upper Limit) / 2
Class Interval Width = Upper Limit - Lower Limit
Cumulative Frequency = Sum of Frequencies up to a certain class

Theorems

Basic properties of Frequency Distribution

Suitable Grade Level

Grades 10-12

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