Question

A diver records the depths, in feet, of her dives. They are:    60, 58, 53, 49, 60 The mean of the data set is 56. Use the equation for variance below, along with the given data set, to answer the following questions. equation for variance What does the numerator evaluate to? What does the denominator evaluate to? The variance equals:

Answer 1

From the given set of data:
 60, 58, 53, 49, 60
the mean is 56
the variance will be found using the formula:
variance=[Σ(x-μ)²]/N
[Σ(x-μ)²]=(60-56)²+(58-56)²+(53-56)²+(49-56)²+(60-56)²
            =16+4+9+49+16
            =94
but N=5
thus
Variance=94/5=18.8

Answer 2

Variance shows the spread of data numbers. The variance of the given data set {60, 58, 53, 49, 60} whose mean is 56 is 18.8.

What is Variance?

Variance is the spread of the numbers of a given data set.

We know that a data set is given to us, whose mean is 56. The formula for the variance of the data can be given as,

Variance = {∑(x-μ)²}÷{N}

Substitute the value,

 =  {(60-56)² + (58-56)² + (53-56)² + (49-56)² + (60-56)² }÷{5}

 =  {(4)² + (2)² + (-3)² + (-7)² + (4)² }÷{5}

 =  {16 + 4 + 9 + 49 + 16}÷{5}

 =  {16 + 4 + 9 + 49 + 16}÷{5}

 = 18.8

Hence, the variance of the given data set {60, 58, 53, 49, 60} whose mean is 56 is 18.8.

Learn more about Variance:

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