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.

Answer 1

Answer:

a)

Leaf       Stem

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)

Digit     Frequency      Relative frequency

0               8                       8/30=0.267

1                6                       6/30=0.2

2               3                        3/30=0.1

3               2                        2/30=0.067

4               3                        3/30=0.1

5               4                        4/30=0.133

6               4                        4/30=0.133

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Total        30                         1.00

Step-by-step explanation:

For this case the first step is order the data from the smallest value to the largest and we have this:

0.2, 0.2, 0.2, 0.3,0.3, 0.4, 0.5, 0.7, 1, 1.2, 1.3, 1.5, 1.5, 1.8, 2, 2.3, 2.5, 3, 3.3, 4

4.5, 4.7, 5, 5.5, 5.6, 5.9, 6, 6, 6, 6.5

Part a

We can create the stem leaf plot like this

Leaf       Stem

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

Part b

We can create a frequency distribution using the digit to the left of the decimal point like this:

Digit     Frequency      Relative frequency

0               8                       8/30=0.267

1                6                       6/30=0.2

2               3                        3/30=0.1

3               2                        2/30=0.067

4               3                        3/30=0.1

5               4                        4/30=0.133

6               4                        4/30=0.133

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Total        30                         1.00