Step 1: Calculate the sum of the dataset

The sum of the dataset can be calculated by multiplying the mean by the number of observations.

So, Sum = Mean * Number of observations = 16 * 10 = 160

Step 2: Correct the error in the dataset

The sum of the dataset after correcting the error is the original sum minus the incorrect observation plus the correct observation.

So, Corrected Sum = Original Sum - Incorrect observation + Correct observation = 160 - 10 + 16 = 166

Step 3: Calculate the corrected mean

The corrected mean is the corrected sum divided by the number of observations.

So, Corrected Mean = Corrected Sum / Number of observations = 166 / 10 = 16.6

Step 4: Calculate the sum of squares of the dataset

The sum of squares of the dataset can be calculated by adding the square of the standard deviation to the square of the mean, multiplied by the number of observations.

So, Sum of squares = (Standard deviation)^2 * Number of observations + Mean^2 * Number of observations = 10^2 * 10 + 16^2 * 10 = 1000 + 2560 = 3560

Step 5: Calculate the corrected sum of squares

The corrected sum of squares is the original sum of squares minus the square of the incorrect observation plus the square of the correct observation.

So, Corrected Sum of squares = Original Sum of squares - Incorrect observation^2 + Correct observation^2 = 3560 - 10^2 + 16^2 = 3560 - 100 + 256 = 3716

Step 6: Calculate the sample variance

The sample variance is the corrected sum of squares divided by the number of observations minus 1, minus the square of the corrected mean.

So, Sample Variance = (Corrected Sum of squares / (Number of observations - 1)) - Corrected Mean^2 = (3716 / (10 - 1)) - 16.6^2 = 412.89 - 275.56 = 137.33

So, the sample variance of the original dataset is 137.33 (correct to 2 decimal places).

Question

Step 1: Calculate the sum of the dataset

The sum of the dataset can be calculated by multiplying the mean by the number of observations.

So, Sum = Mean * Number of observations = 16 * 10 = 160

Step 2: Correct the error in the dataset

The sum of the dataset after correcting the error is the original sum minus the incorrect observation plus the correct observation.

So, Corrected Sum = Original Sum - Incorrect observation + Correct observation = 160 - 10 + 16 = 166

Step 3: Calculate the corrected mean

The corrected mean is the corrected sum divided by the number of observations.

So, Corrected Mean = Corrected Sum / Number of observations = 166 / 10 = 16.6

Step 4: Calculate the sum of squares of the dataset

The sum of squares of the dataset can be calculated by adding the square of the standard deviation to the square of the mean, multiplied by the number of observations.

So, Sum of squares = (Standard deviation)^2 * Number of observations + Mean^2 * Number of observations = 10^2 * 10 + 16^2 * 10 = 1000 + 2560 = 3560

Step 5: Calculate the corrected sum of squares

The corrected sum of squares is the original sum of squares minus the square of the incorrect observation plus the square of the correct observation.

So, Corrected Sum of squares = Original Sum of squares - Incorrect observation^2 + Correct observation^2 = 3560 - 10^2 + 16^2 = 3560 - 100 + 256 = 3716

Step 6: Calculate the sample variance

The sample variance is the corrected sum of squares divided by the number of observations minus 1, minus the square of the corrected mean.

So, Sample Variance = (Corrected Sum of squares / (Number of observations - 1)) - Corrected Mean^2 = (3716 / (10 - 1)) - 16.6^2 = 412.89 - 275.56 = 137.33

So, the sample variance of the original dataset is 137.33 (correct to 2 decimal places).

Knowee AI · Accepted Answer