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g A cell phone company is considering using a new manufacturer to produce batteries for their phones. The company distributes a random sample of cell phones with the new batteries to 13 of their employees to record how long the battery will last with typical usage. The length of time each battery lasts is recorded (in hours) in the set below. LaTeX: \left\{32.3,\:28.8,\:29.1,\:29.5,\:30.8,\:31.0,\:17.5,\:34.5,\:23.5,\:33.0,\:31.7,\:28.6,\:27.4\right\}{ 32.3 , 28.8 , 29.1 , 29.5 , 30.8 , 31.0 , 17.5 , 34.5 , 23.5 , 33.0 , 31.7 , 28.6 , 27.4 } On a blank sheet of paper, find the following information. You may use a calculator, and you may discuss this assignment with your classmates, but you must show all your work (including any formulas or calculations you use), and the work must be your own. Be neat and clearly mark your answer. The range. The mean. The median. Q1 and Q3. The IQR. The variance. The standard deviation.

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Answer:

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Step-by-step explanation:

Given the data:

32.3 , 28.8 , 29.1 , 29.5 , 30.8 , 31.0 , 17.5 , 34.5 , 23.5 , 33.0 , 31.7 , 28.6 , 27.4

Reordered data:

17.5, 23.5, 27.4, 28.6, 28.8, 29.1, 29.5, 30.8, 31.0, 31.7, 32.3, 33.0, 34.5

The mean ; m

Mean, m = Σx /n

Σx = 377.7

n = sample size = 13

m = Σx / n = 377.7 / 13 = 29.05

Median = 1/2(n+1)th term

= 1/2(14) = 7th term = 29.5

Range = maximum - minimum

Range = 34.5 - 17.5 = 17

Lower quartile (Q1) = 1/4(n+1)th term

1/4(14)th term = 3.5th term

(3rd + 4th) / 2

= (27.4 + 28.6) / 2

= 28

Upper quartile (Q3) = 3/4(n+1)th term

3/4(14)th term = 10.5th term

(10th + 11th) / 2

= (31.7 + 32.3) / 2

= 32

IQR = Q3 - Q1

IQR = 32 - 28 = 4

Variance : (V) = Σ(x - m)²/n-1

[(32.3-29.05)^2 +(28.8-29.05)^2 + (29.1 - 29.05)^2 + (29.5-29.05)^2 + (30.8-29.05)^2 + (31.0-29.05)^2 + (17.5 - 29.05)^2 + (34.5-29.05) ^2 + (23.5-29.05)^2 + (33.0-29.05)^2 + (31.7-29.05)^2 + (28.6-29.05)^2 + (27.4 - 29.05)^2] / 12

Variance = 19.76

Standard deviation = sqrt(variance)

Standard deviation = sqrt(19.76)

Standard deviation = 4.45

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