Question

does this help?

112.91113.58114.32 113.94113.50 11.28 112.17 113.95 112.16 114.26 114.19 114.53 112.72 113.49 114.23 112.48 114.84 112.02 114.56 112.79 112.87 111.80 112.36 114.41 114.59 113.79 112.78 114.45 113.44 114.42 114.22 114.51 114.39 112.03 114.40 113.54 114.38 113.12 114.90 112.35 112.68 113.45 114.89 113.74 113.34 111.91 113.75 115.13 112.13 114.17 111.90 112.60 113.04 112.69 114.04 112.49 113.51 113.31 114.68 112.80 1819747019108 2774027161160 824028 9287790278109 1. An industrial equipment maintenance service keeps track of the number of service calls they receive in different categories by week. For a particular category, the number of calls per week for the last 52 weeks is provided in the table below. Develop a frequency diagram based on this data. [8 points 12 12 12 12 10 12 20 12 10 12 10 16 10 10 2. A food processor makes frozen TV dinners. To control costs and provide a consistent product, the company has established specifications for portion sizes in the dinners. A particular entrée has a portion specification of 113.003.00 grams. A QC tech takes a random sample of 60 dinners from the line and carefully weighs the entrée portion, resulting in the following data Develop a histogram for this data. Comment on what it reveals. [12 points] 112.91 112.17 113.95 112.16 114.26 114.19 114.53 112.72 113.49 114.23 113.58 112.48 114.84 112.02 114.56 112.79 112.87 111.80 112.36 114.41 114.32 114.59 113.79 112.78 114.45 113.44 114.42 114.22 114.51 114.39 113.94 112.03 114.40 113.54 114.38 113.12 114.90 112.35 112.68 113.45 113.50 114.89 113.74 113.34 111.91 13.75 115.13 112.13 114.17 111.90 114.28 112.60 113.0 112.69 114.04 112.49 113.51 113.31 114.68 112.80

Answer 1

1) This is a single-valued discrete value ranging from possible values of 7 to 20.

We can make a frequency distribution table first.

For that, we simply count the number of times each value occurs and list it in a tabular form as below.

0 10 6 6 6 9 7 0 4 0 3 0 0 0 1 52 123 56789 789

Then we put it in a frequency diagram as follows with the number of calls per week in the x-axis and the counts in the y-axis.

Frequency Diagram 10 9 0 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of calls per week

2) The data type here is continuous, so we have to make the histogram with intervals.

Number of observations = 60.

First decide the number of class intervals that you are going to have in the histogram.

As a rule of thumb, it is the square root of the number of observations (rounded up). So, $\sqrt{60}$ = 7.75

Let's round it up to 8. So, the number of class intervals = 8

Next, determine the range i.e. difference of maximum and minimum values in the data.

Range = 115.13-111.8 = 3.33

Next, width of the class interval (interval class width) = Range/Number of class intervals = 3.33/8 = 0.42

So, our classes will be as follows:

Classes
111.80-112.21
112.22-112.63
112.64-113.05
113.06-113.47
113.48-113.89
113.90-114.31
114.32-114.73
114.74-115.15

Note that, the class width i.e. 0.42 is the difference between the lower limits of consecutive classes or the upper limits of consecutive classes. It is NOT the difference between upper limit and lower limit of the same class.

Now, the next job is to count the number of observations that fall in each class.

This will give the frequency distribution table:

Classes 111.80-112.21 112.22-112.63 112.64-113.05 113.06-113.47 113.48-113.89 113.90-114.31 114.32-114.73 114.74-115.15 TOTAL Frequency 2 12 60

Plotting these into a graph with the classes in the x-axis and frequency/counts in the y-axis, we have the histogram:

Histogram 14 12 10 111.80-112.21 112.22-112.63 112.64-113.05 113.06-113.47 113.48-113.89 113.90-114.31 114.32-114.73 114.74-115.15 Entree Portion Weight

Allowed portion specification = 113-3 to 113+3 grams = 110 to 116 grams.

From the histogram, we can see that all of the portions measured conform to the specifications. We can also see from the histogram that majority of the portion weights are more than 113 grams. The most common range for the portion weight is 114.32 grams to 114.73 grams where there are 12 observations (20% of the total observations).