Question

The following data represent the length of life in

years, measured to the nearest tenth, of 30 similar fuel
pumps:
2.0 3.0 0.3 3.3 1.3 0.4
0.2 6.0 5.5 6.5 0.2 2.3
1.5 4.0 5.9 1.8 4.7 0.7
4.5 0.3 1.5 0.5 2.5 5.0
1.0 6.0 5.6 6.0 1.2 0.2
(a) Construct a stem-and-leaf plot for the life in years
of the fuel pumps, using the digit to the left of the
decimal point as the stem for each observation.
(b) Set up a relative frequency distribution.
(c) Compute the sample mean, sample range, and sample
standard deviation.

Answer 1

(a) For the stem-and-leaf plot, we need to organise all data in columns, one column is the stem and a second column is the leaf, but in this case, stems are going to be the digits to the left of the decimal point, and leafs are the digits to the right of the decimal point:

Stem Leaf

0 2 2 2 3 3 4 5 7

1 0 2 3 5 5 8

2 0 3 5

3 0 3

4 0 5 7

5 0 5 6 9

6 0 0 0 5

(b) Relative frequency distribution.

Remember that, a relative frequency is calculated dividing the absolute frequency by the total data, in this case, we approximated to the hundredth.

Length of life Absolute Frequency Relative Frequency % Relative Freq.

0.2 3 0.1 10

0.3 2 0.07 7

0.4 1 0.03 3

0.5 1 0.03 3

0.7 1 0.03 3

1.0 1 0.03 3

1.2 1 0.03 3

1.3 1 0.03 3

1.5 2 0.07 7

1.8 1 0.03 3

2.0 1 0.03 3

2.3 1 0.03 3

2.5 1 0.03 3

3.0 1 0.03 3

3.3 1 0.03 3

4.0 1 0.03 3

4.5 1 0.03 3

4.7 1 0.03 3

5.0 1 0.03 3

5.5 1 0.03 3

5.6 1 0.03 3

5.9 1 0.03 3

6.0 3 0.10 10

6.5 1 0.03 3

Total 30

(c)

To calculate the sample mean we need to sum all number, which results: 83.9. Then, we divide this result to the total 30, which result: 2.80.

The sample range is the difference between the highest and the lowest value: 6.5 - 0.2 = 6.3.

The sample standard deviation is calculated trough the following process:

Step 1: Subtract the mean from each number.

Step 2: Square each result.

Step 3: Add the squared deviations.

Step 4: Divide the sum by one less the total.

Step 5: Take the square root, and there you have it.

Doing this steps, the result is 2.22.

This last process is attached: