Which one of the following is the cumulative frequency for the class limit 401-500 from the given data set

Question

Prepp Team · Accepted Answer

Finding Cumulative Frequency for Class Limit 401-500

Understanding how to calculate cumulative frequency is important when working with frequency distributions. The cumulative frequency for a specific class is the sum of the frequencies of that class and all the classes that come before it in the distribution.

Let's look at the given data set showing class limits and their corresponding frequencies:

S. No.	Class Limit	Frequency
1	101-200	4
2	201-300	12
3	301-400	24
4	401-500	40
5	501-600	16
6	601-700	12
7	701-800	10
8	801-900	5
9	901-1000	2

To find the cumulative frequency for the class limit 401-500, we need to add the frequencies of all classes up to and including 401-500.

Here is the step-by-step calculation for the cumulative frequency of each class:

For the class 101-200, the cumulative frequency is simply its own frequency: 4.
For the class 201-300, the cumulative frequency is the sum of the frequency of 101-200 and 201-300: ${4 + 12 = 16}$.
For the class 301-400, the cumulative frequency is the sum of the frequencies of the first three classes: ${4 + 12 + 24 = 40}$.
For the class 401-500, the cumulative frequency is the sum of the frequencies of the first four classes: ${4 + 12 + 24 + 40}$.

Let's perform the addition for the class limit 401-500:

Cumulative frequency for 401-500 = Frequency(101-200) + Frequency(201-300) + Frequency(301-400) + Frequency(401-500)

Cumulative frequency for 401-500 = ${4 + 12 + 24 + 40}$

Cumulative frequency for 401-500 = ${16 + 24 + 40}$

Cumulative frequency for 401-500 = ${40 + 40}$

Cumulative frequency for 401-500 = ${80}$

So, the cumulative frequency for the class limit 401-500 is 80.

Cumulative Frequency Table

We can construct a cumulative frequency column in the table for clarity:

Class Limit	Frequency	Cumulative Frequency
101-200	4	4
201-300	12	$4 + 12 = 16$
301-400	24	$16 + 24 = 40$
401-500	40	$40 + 40 = 80$
501-600	16	$80 + 16 = 96$
601-700	12	$96 + 12 = 108$
701-800	10	$108 + 10 = 118$
801-900	5	$118 + 5 = 123$
901-1000	2	$123 + 2 = 125$

Looking at the table, the cumulative frequency corresponding to the class limit 401-500 is indeed 80.

Revision Table: Frequency Distribution Concepts

Concept	Definition	How to Calculate
Frequency	The number of observations that fall within a specific class interval.	Count the occurrences in the data.
Class Limit	The upper and lower values that define a class interval. (e.g., 401 is lower limit, 500 is upper limit).	Provided in the data or determined from range and number of classes.
Cumulative Frequency	The total frequency of a given class and all preceding classes.	Sum the frequency of the current class and the cumulative frequency of the previous class.
Cumulative Frequency Distribution	A table showing the cumulative frequency for each class interval.	Calculate cumulative frequency for all classes.

Additional Information: Types of Frequency Distributions

Besides simple frequency distribution and cumulative frequency distribution, there are other related concepts:

Relative Frequency Distribution: Shows the proportion (or percentage) of observations in each class. Calculated as (Class Frequency / Total Frequency).
Cumulative Relative Frequency Distribution: Shows the cumulative proportion (or percentage) of observations up to and including a particular class. Calculated by summing relative frequencies or dividing cumulative frequency by total frequency.

Cumulative frequency distributions are particularly useful for finding percentiles, quartiles, and medians, and for creating ogive graphs.