Question

The normal monthly precipitation (in inches) for August is listed for 12 different U.S. cities. Find the variance for this data, rounding to one more decimal place than is present in
the original data.

3.5 1.6 2.4 3.7 4.1 3.9
10 3.6 4.2 3.4 3.7 2.2

Answer 1

The variance is 1.8

Step-by-step explanation:

The formula for variance is;

S²= ∑ (x₁-x')² / n-1

where;

S²=variance

x₁= an x term in the data set

x'=sample mean of data set

n= number of data set

For a table as;

x₁        x'         x₁-x'        (x₁-x')²

3.5                 -0.4          0.16

1.6                  -2.3          5.29

2.4                  -1.5           2.25

3.7                  -0.2          0.04

4.1                    0.2           0.04

3.9                   0.0           0.00

10                    -2.9           8.41

3.6                  -0.3           0.09

4.2                   0.3           0.09

3.4                   -0.5           0.25

3.7                   -0.2           0.04

2.2                   -1.7            2.89

∑46.3  x' 3.9                  ∑ 19.55

x'=46.3/12 = 3.9

Given n=12, hence n-1 =12-1 = 11

19.55/11 =1.777

S²=1.8

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