Battery Lifetimes: Mean, Variance & Standard Deviation

Chapter 3, Problem 25

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QUESTION:

Eighty randomly selected batteries were tested to determine their lifetimes (in hours). The following frequency distribution was obtained. Find the variance and standard deviation for the data.

Class boundaries

Frequency

62.5–73.5

5

73.5–84.5

14

84.5–95.5

18

95.5–106.5

25

106.5–117.5

12

117.5–128.5

6

Can it be concluded that the lifetimes of these brands of batteries are consistent?

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QUESTION:

Eighty randomly selected batteries were tested to determine their lifetimes (in hours). The following frequency distribution was obtained. Find the variance and standard deviation for the data.

Class boundaries

Frequency

62.5–73.5

5

73.5–84.5

14

84.5–95.5

18

95.5–106.5

25

106.5–117.5

12

117.5–128.5

6

Can it be concluded that the lifetimes of these brands of batteries are consistent?

ANSWER:

Step 1 of 2

We have the data of lifetimes of batteries.

Class boundaries

Midpoint \(\left(x_{i}\right)\)

Frequency

62.5–73.5

68

5

73.5–84.5

79

14

84.5–95.5

90

18

95.5–106.5

101

25

106.5–117.5

112

12

117.5–128.5

123

6

The claim is to find the variance and standard deviation.

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Battery Lifetimes: Mean, Variance & Standard Deviation
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Discover the nuances of analyzing battery lifetime data through mean, variance, and standard deviation computations. Using class boundaries, midpoints, and frequencies, gain insights into the dispersion of battery lifespans and the average deviation from the mean.


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