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The Marks of 10 students in an English test are given below: 10, 21, 22, 35, 37, 13, 16, 18, 24, 34  What is the population standard deviation of the data?

Question

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Solution

Sure, here are the steps to calculate the population standard deviation:

  1. First, calculate the mean (average) of the data set. Add all the numbers together and then divide by the number of items in the set.

    (10 + 21 + 22 + 35 + 37 + 13 + 16 + 18 + 24 + 34) / 10 = 23

  2. Next, subtract the mean from each number in the data set and then square the result. This is called the "squared difference".

    (10-23)^2 = 169 (21-23)^2 = 4 (22-23)^2 = 1 (35-23)^2 = 144 (37-23)^2 = 196 (13-23)^2 = 100 (16-23)^2 = 49 (18-23)^2 = 25 (24-23)^2 = 1 (34-23)^2 = 121

  3. Now, find the average of these squared differences. This is called the "variance".

    (169 + 4 + 1 + 144 + 196 + 100 + 49 + 25 + 1 + 121) / 10 = 81

  4. Finally, take the square root of the variance to get the standard deviation.

    √81 = 9

So, the population standard deviation of the data is 9.

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