Calculate Mean Median and Mode for Grouped Frequency Distribution

Published on September 14, 2026

Statistics

Learn how to compute the mean, median, mode, percentiles, and percentages for grouped frequency distribution data from two comprehensive statistical problems step by step.

Question

Solve 6 and 7

Answer

To solve these problems, we will use the formulas for grouped data.

Problem 6

First, we construct a table to find the midpoints (

), the product of frequency and midpoint (

), and the cumulative frequency (

Sales (in Thousand Taka)	Frequency ()	Midpoint ()		Cumulative Frequency ()







Total

a. Compute mean, median and mode of sales.

Mean ():
Median:
The median class is the class where the value falls. Looking at , the value is in the class.
Formula:
Where .
Mode:
The modal class is the class with the highest frequency, which is ().
Formula:
Where .

b. Fifty percent of the motor cycles were sold for less than what amount?
This is the definition of the median.

c. Compute selling range of the central 50% cycles?
The central 50% range is the interval between the

percentile (

) and the

percentile (

position: value. Class: .
position: value. Class: .

Problem 7

Weight (g)	Frequency ()	Midpoint ()		Cumulative Frequency ()







Total

a. Compute mean, median and mode of weights of mangoes.

Mean ():
Median:
value. Class: .
Mode:
Modal class: ().

b. Percentage unsuitable/suitable for export (unsuitable if g).

Unsuitable: We need the count for weights .
From table, class contains values up to . We must interpolate for .
Count up to .
Count in class up to : .
Total unsuitable .

c. How many mangoes have weights less than 500 gm? 500 gm and more?
Based on the table, the lowest class starts at

Less than 500 gm:
500 gm and more:

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