Answer :
To find the variance of the given set of data, follow these steps:
1. List the Data:
The data set is: 18, 16, 12, 2, 11.
2. Calculate the Mean:
First, find the mean (average) of the data.
[tex]\[
\text{Mean} = \frac{18 + 16 + 12 + 2 + 11}{5} = \frac{59}{5} = 11.8
\][/tex]
3. Calculate Each Deviation from the Mean:
Subtract the mean from each data point to find the deviation of each value from the mean:
- [tex]\(18 - 11.8 = 6.2\)[/tex]
- [tex]\(16 - 11.8 = 4.2\)[/tex]
- [tex]\(12 - 11.8 = 0.2\)[/tex]
- [tex]\(2 - 11.8 = -9.8\)[/tex]
- [tex]\(11 - 11.8 = -0.8\)[/tex]
4. Square Each Deviation:
Square each of the deviations:
- [tex]\(6.2^2 = 38.44\)[/tex]
- [tex]\(4.2^2 = 17.64\)[/tex]
- [tex]\(0.2^2 = 0.04\)[/tex]
- [tex]\((-9.8)^2 = 96.04\)[/tex]
- [tex]\((-0.8)^2 = 0.64\)[/tex]
5. Calculate the Variance:
The variance is the average of these squared deviations. Since this is sample data, use [tex]\(n-1\)[/tex] (where [tex]\(n\)[/tex] is the number of data points) for the calculation.
[tex]\[
\text{Variance} = \frac{38.44 + 17.64 + 0.04 + 96.04 + 0.64}{5 - 1} = \frac{152.8}{4} = 38.2
\][/tex]
6. Rounding the Result:
Since all original data had no decimal places, round the variance to one decimal place.
[tex]\[
\text{Variance (rounded)} = 38.2
\][/tex]
Therefore, the variance of the data set is [tex]\(38.2\)[/tex].
1. List the Data:
The data set is: 18, 16, 12, 2, 11.
2. Calculate the Mean:
First, find the mean (average) of the data.
[tex]\[
\text{Mean} = \frac{18 + 16 + 12 + 2 + 11}{5} = \frac{59}{5} = 11.8
\][/tex]
3. Calculate Each Deviation from the Mean:
Subtract the mean from each data point to find the deviation of each value from the mean:
- [tex]\(18 - 11.8 = 6.2\)[/tex]
- [tex]\(16 - 11.8 = 4.2\)[/tex]
- [tex]\(12 - 11.8 = 0.2\)[/tex]
- [tex]\(2 - 11.8 = -9.8\)[/tex]
- [tex]\(11 - 11.8 = -0.8\)[/tex]
4. Square Each Deviation:
Square each of the deviations:
- [tex]\(6.2^2 = 38.44\)[/tex]
- [tex]\(4.2^2 = 17.64\)[/tex]
- [tex]\(0.2^2 = 0.04\)[/tex]
- [tex]\((-9.8)^2 = 96.04\)[/tex]
- [tex]\((-0.8)^2 = 0.64\)[/tex]
5. Calculate the Variance:
The variance is the average of these squared deviations. Since this is sample data, use [tex]\(n-1\)[/tex] (where [tex]\(n\)[/tex] is the number of data points) for the calculation.
[tex]\[
\text{Variance} = \frac{38.44 + 17.64 + 0.04 + 96.04 + 0.64}{5 - 1} = \frac{152.8}{4} = 38.2
\][/tex]
6. Rounding the Result:
Since all original data had no decimal places, round the variance to one decimal place.
[tex]\[
\text{Variance (rounded)} = 38.2
\][/tex]
Therefore, the variance of the data set is [tex]\(38.2\)[/tex].
