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✅Question :

Calculate the standard deviation and co-efficient of variation: Mark secured No. of stds 0-20 2 20-40 8 40-60 16 60-80 10 80-100 4

✅Answer :

To calculate the standard deviation and coefficient of variation, we’ll need to follow these steps:

- Calculate the mean (average) of the data.
- Calculate the squared differences between each data point and the mean.
- Calculate the variance by finding the average of the squared differences.
- Take the square root of the variance to get the standard deviation.
- Calculate the coefficient of variation by dividing the standard deviation by the mean and multiplying by 100 (to get a percentage).

Let’s begin:

**Data:**

`Mark Range | No. of Students 0-20 | 2 20-40 | 8 40-60 | 16 60-80 | 10 80-100 | 4`

Step 1: Calculate the mean (average):

`Mean = (0 + 20 + 40 + 60 + 80) / 5 = 40`

Step 2: Calculate the squared differences between each data point and the mean:

`Squared Differences = (0 - 40)^2 + (20 - 40)^2 + (40 - 40)^2 + (60 - 40)^2 + (80 - 40)^2 = 1600 + 400 + 0 + 400 + 1600 = 4000`

Step 3: Calculate the variance by finding the average of the squared differences:

`Variance = 4000 / 5 = 800`

Step 4: Take the square root of the variance to get the standard deviation:

`Standard Deviation = √800 ≈ 28.28`

Step 5: Calculate the coefficient of variation:

`Coefficient of Variation = (Standard Deviation / Mean) * 100 = (28.28 / 40) * 100 ≈ 70.7%`

So, the standard deviation is approximately 28.28, and the coefficient of variation is approximately 70.7%.

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