Question

Calculate mean, median and mode from the following data.

Class Interval Frequency
3-4 3
4-5 7
5-6 22
6-7 60
7-8 85
8-9 32
9-10 8

 

07 Aug 2023
Answer :
Word Count : 827

To calculate the mean, median, and mode from the given frequency distribution, we need to perform the following steps:

  1. Calculate the Midpoint of each class interval.
  2. Calculate the Product of Midpoint and Frequency for each class interval to find the weighted values.
  3. Calculate the Total Frequency and Total Weighted Value.
  4. Calculate the Mean using the formula: Mean = Total Weighted Value / Total Frequency.
  5. Find the Median by locating the middle value or values in the dataset.
  6. Find the Mode, which is the value that appears most frequently.

Let's go through these steps one by one:

Step 1: Calculate Midpoint The midpoint of a class interval can be calculated by taking the average of the lower and upper limits of the interval.

Class Interval Frequency Midpoint
3-4 3 (3 + 4) / 2 = 3.5
4-5 7 (4 + 5) / 2 = 4.5
5-6 22 (5 + 6) / 2 = 5.5
6-7 60 (6 + 7) / 2 = 6.5
7-8 85 (7 + 8) / 2 = 7.5
8-9 32 (8 + 9) / 2 = 8.5
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