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Less Than Cumulative Frequency

Less than cumulative frequency is the running total of frequencies obtained by adding the frequency of a particular class interval to the sum of frequencies of all preceding classes. It indicates the total number of observations that fall below the upper limit of a specific class.

Key Concepts

It is constructed by sequentially adding the frequencies from the lowest class interval down to the highest class interval.

When represented graphically, these cumulative frequencies are plotted against the upper class limits to form a less than ogive curve.

The final cumulative frequency value in the distribution always equals the total number of observations, denoted as N.

Formula & Equation

cf_{n} = cf_{n-1} + f_{n}

cf_{n} is the less than cumulative frequency of the nth class, cf_{n-1} is the cumulative frequency of the previous class, and f_{n} is the absolute frequency of the current class.

Common Misconceptions

Myth: Students often plot the less than cumulative frequency against the lower limit of the class interval when drawing an ogive.

Fact: It must always be plotted against the upper limit of the class interval, because the cumulative value represents all observations strictly less than that upper boundary.

Real World Applications

A teacher calculating how many students scored less than 80 marks in a mathematics test to identify the overall performance level of the class.

A company analyzing salary data to find out the total number of employees earning less than 50000 rupees per month for budget planning.

Frequently Asked Questions

How is less than cumulative frequency used to find the median?

It helps identify the median class, which is the class interval whose cumulative frequency is strictly greater than and nearest to \frac{N}{2}, where N is the total frequency.

What is the difference between less than and more than cumulative frequency?

Less than cumulative frequency adds frequencies from the lowest class to the highest, while more than cumulative frequency adds them from the highest class to the lowest.

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