The variance of a sample is a measure of how much the values in the sample differ from the mean. It is calculated by taking the average of the squared differences from the mean.

Here are the steps to calculate the sample variance:

1. Calculate the mean (average) of the original data set:
(76 + 84 + 30 + 78 + 68 + 87 + 59 + 88 + 98) / 9 = 74.22

2. Add 2 to each data point in the set:
78, 86, 32, 80, 70, 89, 61, 90, 100

3. Calculate the new mean:
(78 + 86 + 32 + 80 + 70 + 89 + 61 + 90 + 100) / 9 = 76.22

4. Subtract the new mean from each data point, square the result, and then average these squared differences. This is the variance.

However, adding a constant to each data point in a data set does not change the variance. This is because variance is a measure of how spread out the numbers are from the mean, and adding a constant to each number does not change their spread.

So, the variance of the new data set is the same as the variance of the original data set.

To calculate the variance of the original data set:

1. Subtract the mean from each data point and square the result:
(76-74.22)^2, (84-74.22)^2, (30-74.22)^2, (78-74.22)^2, (68-74.22)^2, (87-74.22)^2, (59-74.22)^2, (88-74.22)^2, (98-74.22)^2

2. Add up these squared differences:
3.14, 95.56, 1961.57, 14.11, 38.61, 163.14, 231.17, 190.56, 564.11

3. Divide by the number of data points minus 1 (this is what makes it the sample variance rather than the population variance):
(3.14 + 95.56 + 1961.57 + 14.11 + 38.61 + 163.14 + 231.17 + 190.56 + 564.11) / 8 = 407.61

So, the sample variance of the retail prices, even after adding 2 rupees to all the retail prices, is 407.61 (to 2 decimal places).

Question

The variance of a sample is a measure of how much the values in the sample differ from the mean. It is calculated by taking the average of the squared differences from the mean.

Here are the steps to calculate the sample variance:

1. Calculate the mean (average) of the original data set: 
   (76 + 84 + 30 + 78 + 68 + 87 + 59 + 88 + 98) / 9 = 74.22

2. Add 2 to each data point in the set: 
   78, 86, 32, 80, 70, 89, 61, 90, 100

3. Calculate the new mean: 
   (78 + 86 + 32 + 80 + 70 + 89 + 61 + 90 + 100) / 9 = 76.22

4. Subtract the new mean from each data point, square the result, and then average these squared differences. This is the variance.

However, adding a constant to each data point in a data set does not change the variance. This is because variance is a measure of how spread out the numbers are from the mean, and adding a constant to each number does not change their spread.

So, the variance of the new data set is the same as the variance of the original data set.

To calculate the variance of the original data set:

1. Subtract the mean from each data point and square the result: 
   (76-74.22)^2, (84-74.22)^2, (30-74.22)^2, (78-74.22)^2, (68-74.22)^2, (87-74.22)^2, (59-74.22)^2, (88-74.22)^2, (98-74.22)^2

2. Add up these squared differences: 
   3.14, 95.56, 1961.57, 14.11, 38.61, 163.14, 231.17, 190.56, 564.11

3. Divide by the number of data points minus 1 (this is what makes it the sample variance rather than the population variance): 
   (3.14 + 95.56 + 1961.57 + 14.11 + 38.61 + 163.14 + 231.17 + 190.56 + 564.11) / 8 = 407.61

So, the sample variance of the retail prices, even after adding 2 rupees to all the retail prices, is 407.61 (to 2 decimal places).

Knowee AI · Accepted Answer