Question

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.
{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.

1. The range.
2. The mean.
3. The median.
4.Q1 and Q3.
5. The IQR.
6. The variance.
7. The standard deviation.
8. Identify any outliers.

Answer 1

Answer:

1. The range = 17

2. The mean = 29.053846153846

3. The median = 29.5

4.i) Q1 = 28

ii) Q3 = 32

5. The IQR = 4

6. The variance = 19.7626923

7. The standard deviation = 4.445524975

8. Identify any outliers = 17.5

Step-by-step explanation:

We are given this random samples of 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}

First step before solving any of the question is we rearrange the numbers from lowest to highest

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

1. The range

This is the difference between the Maximum value and the Minimum value in a given data set.

Maximum value = 34.5

Minimum value = 17.5

Range = 34.5 - 17.5

= 17

2. The mean

Mean = Sum of terms/Number of terms

= 17.5 + 23.5 + 27.4 + 28.6 + 28.8 + 29.1 +29.5 + 30.8 + 31.0 +31.7 +32.3 +33.0 +34.5/13

= 377.7/13

= 29.053846153846

3. The median

The formula for Median = 1/2(n + 1)th value

n = 13

= 1/2(13 + 1)th value

= 1/2(14)th value

= 7th value.

The 7th value for the data set = 29.5

4.i) Q1 means the First Quartile

The formula for First Quartile

= 1/4(n + 1)th value

= 1/4(13 + 1)th value

= 14/4 th value

= 3.5 th value

This means, the first quartile is between the 3rd and 4th value

3rd value = 27.4

4th value = 28.6

Q1 = 27.4 +28.6/2

= 56/2

= 28

ii) Q3

The Formula for Third Quartile

= 3/4(n + 1)th value

= 3/4(13 + 1)th value

= 42/4 th value

= 10.5th value

This means, the first quartile is between the 10th and 11th value

10th value = 31.7

11th value = 32.3

Q1 = 31.7 +32.3/2

= 64/2

= 32

5. The IQR

IQR = Interquartile range. It is the difference between Q3 and Q1

= 32 - 28

= 4

6. The sample variance

The formula = (x -mean)²/n - 1

= [(17.5 -29.053846153846)² + (23.5 -29.053846153846)² + (27.4 -29.053846153846)² + (28.6 -29.053846153846)² + (28.8 -29.053846153846)² + (29.1 -29.053846153846)² + (29.5 -29.053846153846)² +(30.8 -29.053846153846)² + (31.0 -29.053846153846)² + (31.7 -29.053846153846)² +(32.3 -29.053846153846)² +(33.0 -29.053846153846)² +(34.5 -29.053846153846)² ] /13 - 1

= [133.4913609+ 30.8452071 +2.735207101 +0.2059763313 + 0.0644378698 + 0.002130177514 + 0.1990532545 + 3.049053254 + 3.787514792 + 7.002130177 + 10.53751479 + 15.57213018 +29.66059171] /12

= 237.1523076/12

= 19.7626923

7. The standard deviation =

= √Variance

= √ 19.7626923

= 4.445524975

8. Identify any outliers

Outliers are number in a data set that varies different from the other data. It can be a extremely large or extremely small.

The outliers in the data set = 17.5