Answer :
The variance of the given data 147, 141, 120, 124, and 128 is 106.
What do we mean by the variance of data?
The variance of data points is a measure of how they deviate from the mean. The variance of a collection of data (numbers) is a measure of how much they differ from their mean (average) value. The term "variance" refers to determining the anticipated variation from the actual value.
Variance is often represented by the symbol σ², and its formula is:
σ² = (∑(x-μ)²)/N, where x represents the data points, μ represents the mean of the data, and N represents the number of observations.
How do we solve the given question?
We are asked to find the variance of the given data: 147, 141, 120, 124, 128.
We will use the formula:
σ² = (∑(x-μ)²)/N, where x represents the data points, μ represents the mean of the data, and N represents the number of observations.
N = 5.
Mean μ can be calculated using the formula: μ = (∑x)/N
μ = (147 + 141 + 120 + 124 + 128)/5 = 660/5 = 132.
Now we can calculate the variance,
σ² = (∑(x-μ)²)/N
or, σ² = {(147-132)² + (141-132)² + (120-132)² + (124-132)² + (128-132)²}/5
or, σ² = {(15)² + (9)² + (-12)² + (-8)² + (-4)²}/5
or, σ² = {225 + 81 + 144 + 64 + 16}/5
or, σ² = 530/5
or, σ² = 106.
∴ The variance of the given data 147, 141, 120, 124, and 128 is 106.
Learn more about the variance of data at
https://brainly.com/question/1851450
#SPJ2
