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Calculate the standard deviation and co-efficient of variation

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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:

  1. Calculate the mean (average) of the data.
  2. Calculate the squared differences between each data point and the mean.
  3. Calculate the variance by finding the average of the squared differences.
  4. Take the square root of the variance to get the standard deviation.
  5. 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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