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Chapter 12: Q10. (page 797)

Find the mean, variance, and standard deviation to the nearest tenth for each set of data.

4,5,5,6,6,8,9,10

Short Answer

Expert verified

The mean, variance and standard variation of the given data set is6.625,3.984 and 2 respectively.

Step by step solution

01

Step 1. Find the mean.

To find the mean, add the numbers and then divide by the number of values in the data set.

x¯=4+5+5+6+6+8+9+108=538=6.625

02

Step 2. Find the variance.

To find the variance, square the difference between each number and the mean. Then add the squares, and divide by the number of values.

σ2=(4−6.63)2+(5−6.63)2+(5−6.63)2+(6−6.63)2+(6−6.63)2+(8−6.63)2+(9−6.63)2+(10−6.63)28=(−2.625)2+(−1.625)2+(−1.625)2+(−0.625)2+(−0.625)2+(1.375)2+(2.375)2+(3.375)28=6.890625+2.640625+2.640625+0.390625+0.390625+1.890625+5.640625+11.3906258=31.8758=3.984

03

Step 3. Find the standard deviation.

To find the standard deviation, take square root of the variance.

σ2=3.984σ=3.984=1.996≈2

Therefore, the mean, variance and standard variation of the given data set is6.625,3.984 and 2 respectively.

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Most popular questions from this chapter

Identify each sample as biased or unbiased. Explain your reasoning.

The local library asks everyone who checks out a book if they also used the computers at the library.

To predict whether or not an issue on a ballot will pass or fail, a committee randomly calls 250 houses with area codes that are inside the voting district and asks the opinions of registered voters. Based on these efforts, the committee determines that 71%±2.5%of the voting population supports the issue. The committee concludes that the issue will pass.

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Evaluate the expression.

C10, 3

Solve each equation. State any extraneous solutions.

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