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Cumulative Frequency

Cumulative frequency is the running total of frequencies in a data set up to a specific class interval. It is calculated by adding the frequency of the current class to the sum of the frequencies of all preceding classes. This statistical measure helps determine the number of observations that fall above or below a particular value.

Key Concepts

There are two types of cumulative frequencies: 'less than' type, which adds frequencies from the lowest class to the highest, and 'more than' type, which adds from the highest class to the lowest.
It is a crucial step in finding the median of grouped data, as it helps identify the median class.
Cumulative frequencies are plotted on a graph against class boundaries to create a cumulative frequency curve, commonly known as an ogive.

Formula & Equation

cfn=āˆ‘i=1nfi=f1+f2+ā‹Æ+fncf_n = \sum_{i=1}^{n} f_i = f_1 + f_2 + \dots + f_n

cf_n is the cumulative frequency of the n-th class, and f_i is the frequency of the i-th class interval.

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Common Misconceptions

Myth: Students often confuse cumulative frequency with simple frequency when reading data tables.
Fact: Simple frequency represents the count of items in a single specific class interval, whereas cumulative frequency represents the accumulated total of items up to that class interval.

Real World Applications

A teacher calculating the total number of students who scored less than 75 marks in a mathematics test to determine how many need remedial classes.
A company tracking its total cumulative sales month by month to see if they have reached their annual target by the third quarter.

Frequently Asked Questions

How do you find the cumulative frequency of grouped data?
To find the cumulative frequency, keep a running total by adding the frequency of each class interval to the sum of the frequencies of all the previous intervals.
Why is cumulative frequency important for finding the median?
Cumulative frequency helps locate the median class, which is the class interval where the cumulative frequency first exceeds half of the total number of observations (N/2).

Keep Learning

Cumulative Frequency DistributionMedianOgive