High School

The amount of time (in seconds) needed to complete a critical task on an assembly line was measured for a sample of 50 assemblies. The data are as follows:

30.3, 34.5, 31.1, 30.9, 33.7, 31.9, 33.1, 31.1, 30.0, 32.7,
34.4, 30.1, 34.6, 31.6, 32.4, 32.8, 31.0, 30.2, 30.2, 32.8,
31.1, 30.7, 33.1, 34.4, 31.0, 32.2, 30.9, 32.1, 34.2, 30.7,
30.7, 30.7, 30.6, 30.2, 33.4, 36.8, 30.2, 31.5, 30.1, 35.7,
30.5, 30.6, 30.2, 31.4, 30.7, 30.6, 37.9, 30.3, 34.1, 30.4

a. Draw a stem-and-leaf display.
b. Draw a histogram.
c. Describe the histogram.

Answer :

The stem and leaf for the data values is

30 | 0 1 1 2 2 2 2 2 3 3 4 5 6 6 6 7 7 7 7 7 9 9

31 | 0 0 1 1 1 4 5 6 9

32 | 1 2 4 7 8 8

33 | 1 1 4 7

34 | 1 2 4 4 5 6

35 | 7

36 | 8

37 | 9

How to draw a stem and leaf for the data values

From the question, we have the following parameters that can be used in our computation:

Data values:

30.3 34.5 31.1 30.9 33.7 31.9 33.1 31.1 30.0 32.7 34.4 30.1 34.6 31.6 32.4 32.8 31.0 30.2 30.2 32.8 31.1 30.7 33.1 34.4 31.0 32.2 30.9 32.1 34.2 30.7 30.7 30.7 30.6 30.2 33.4 36.8 30.2 31.5 30.1 35.7 30.5 30.6 30.2 31.4 30.7 30.6 37.9 30.3 34.1 30.4

Sort in order of tenths

So, we have

30.0 30.1 30.1 30.2 30.2 30.2 30.2 30.2 30.3 30.3 30.4 30.5 30.6 30.6 30.6 30.7 30.7 30.7 30.7 30.7 30.9 30.9

31.0 31.0 31.1 31.1 31.1 31.4 31.5 31.6 31.9

32.1 32.2 32.4 32.7 32.8 32.8

33.1 33.1 33.4 33.7

34.1 34.2 34.4 34.4 34.5 34.6

35.7

36.8

37.9

Next, we draw the stem and leaf as follows:

a | .b

Where

a = stem

b = leaf

number = a.b

Using the above as a guide, we have the following:

Stem | Leaf

------- | -----

30 | 0 1 1 2 2 2 2 2 3 3 4 5 6 6 6 7 7 7 7 7 9 9

31 | 0 0 1 1 1 4 5 6 9

32 | 1 2 4 7 8 8

33 | 1 1 4 7

34 | 1 2 4 4 5 6

35 | 7

36 | 8

37 | 9

The histogram is attached and it shows that the task time is generally distributed between 30 and 35 seconds, with a peak at 30 seconds.

And most assemblies taking between 30 and 32 seconds to complete.

There is a small number of assemblies that took significantly longer than this, but these are outliers.

Read more about stem leaf plot at

brainly.com/question/8649311

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