Question

standard deviation of 10 observations is 3 units if each of the 10 observations is divided by 2 variance of new set of data will be

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The variance of the new set of data will be 9/4.

Given: The standard deviation of 10 observations is 3 units and

each of the 10 observations is divided by 2

To Find: The variance of a new set of data

Solution:

1. Standard deviation is the square root of the Arithmetic means of the squares of the deviations measured from the arithmetic mean of the data.

2. Hence, the deviations are changed whenever there's a multiplication or division to one or all the sets of observations.

3. Since, we need division here so we can say that if each observation is divided by a number 'n', then the whole standard deviation becomes 1/nth of the prior standard deviation.

4. We also know that variance is the square of the standard deviation of a particular set of data.

Coming to the numerical,

Standard deviation = 3 units and each observation is divided by 2

Therefore, from point (3), we get;

New Standard deviation = 3/2

Now since we need the variance of the new set of data, so from point (4);

variance = (new standard deviation)^2

               = (3/2)^2

               = 9/4

Hence, the variance of the new set of data will be 9/4.

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