Question

Calculate the variance for the data set then round the answer to the nearest hundred. 10,19,21,28,12,20,16

Answer 1

To calculate the variance for the data set \(10, 19, 21, 28, 12, 20, 16\), follow these steps:

1. **Calculate the mean**:

\[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{10 + 19 + 21 + 28 + 12 + 20 + 16}{7} = \frac{126}{7} = 18
\]

2. **Calculate the squared differences from the mean**:

\[
(10 - 18)^2 = (-8)^2 = 64
\]
\[
(19 - 18)^2 = (1)^2 = 1
\]
\[
(21 - 18)^2 = (3)^2 = 9
\]
\[
(28 - 18)^2 = (10)^2 = 100
\]
\[
(12 - 18)^2 = (-6)^2 = 36
\]
\[
(20 - 18)^2 = (2)^2 = 4
\]
\[
(16 - 18)^2 = (-2)^2 = 4
\]

3. **Sum the squared differences**:

\[
64 + 1 + 9 + 100 + 36 + 4 + 4 = 218
\]

4. **Calculate the variance**:
Since this is a sample, we use \(n - 1\) (where \(n\) is the number of data points) for the denominator:

\[
\text{Variance} = \frac{\text{Sum of squared differences}}{n - 1} = \frac{218}{7 - 1} = \frac{218}{6} \approx 36.3333
\]

5. **Round to the nearest hundred**:

Since \(36.3333\) rounded to the nearest hundred is \(0\).

Thus, the variance of the data set rounded to the nearest hundred is **0**.