Question

Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Her steps for finding the variance are shown below.

Answer 1

Answer with explanation:

The Given data set having 5 variate arranged in ascending order = {46,78,87,89,90}

Mean of a data set

        $=\frac{\text{Sum of all the observation}}{\text{total number of variate in the data set}}$

Mean of the given data set

          $=\frac{46+78+89+87+90}{5}\\\\=\frac{390}{5}=78$

→Emi has calculated the mean Correctly which is 78.

Now to calculate variance

1. Square of  Absolute difference between mean and each variate

a. | 78-46|²=32² =1024

b. | 78 - 78 |²=0²=0

c. | 89-78|²=11²=121

d. | 87-78 |²=9²=81

e. | 90-78|²=12²=144

The new data set obtained is ={ 0,81,121,144,1024}

Variance    

$=\frac{\text{Sum of each variate in the new data set}}{\text{Total number of variate in the data set}-1}\\\\=\frac{0+81+121+144+1024}{5-1}\\\\=\frac{1370}{4}\\\\=342.5$  

Variance = 342.5  

Answer 2

Answer:

the answer would be the third choice, she put the negative sign for the 32 outside the parenthesis

Step-by-step explanation: