Question

an automotive service company has franchises in two different parts of a city. the number of oil changes made daily, for 25 days, is given below. complete parts a) through f) below.

east store
37 58 27 32 43
20 37 29 25 32
44 29 54 38 54
39 69 37 44 46
15 27 51 42 46

west store
42 43 43 40 34
42 37 39 42 32
39 41 42 36 48
28 30 37 43 33
36 49 31 42 46

c) using the histogram, determine which store appears to have a greater mean, or do the means appear about the same? explain.
a. the west store appears to have a greater mean since its histogram is centered further to the right than the east stores histogram is.
b. the east store appears to have a greater mean since its histogram is centered further to the right than the west stores histogram is.
c. the stores appear to have approximately the same mean since both histograms are centered around the same point.
d. it is impossible to make an inference about the means from the histograms alone.

d) using the histogram, determine which store appears to have the greater standard deviation. explain.
a. the west store appears to have a greater standard deviation since its histogram is wider than the east stores histogram is.
b. the east store appears to have a greater standard deviation since its histogram is wider than the west stores histogram is.
c. the stores appear to have approximately the same standard deviation since both histograms have the same width.
d. it is impossible to make an inference about the standard deviations from the histograms alone.

e) calculate the mean for each store and determine whether your answer in part c) was correct.
the mean for the east store is and the mean for the west store is . these values consistent with the answer in part c).
(round to two decimal places as needed.)

Explanation:

Analyze the histogram centers for part c

Using the Histogram Interpretation knowledge point
The histogram for the East Store is centered around 40, and the histogram for the West Store is also centered around 40. Since both histograms are centered around the same point, the stores appear to have approximately the same mean. Thus, the correct option is C.

Analyze the histogram widths for part d

Using the Histogram Interpretation and Standard Deviation knowledge points
The histogram for the East Store has data values ranging from 15 to 69 (a wider spread), whereas the West Store has data values ranging from 28 to 49 (a narrower spread). Since the East Store's histogram is wider, it appears to have a greater standard deviation. Thus, the correct option is B.

Calculate the mean for the East Store

Using the Mean Calculation knowledge point

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Calculate the mean for the West Store

Using the Mean Calculation knowledge point

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Compare calculated means with part c

Using the Mean Calculation knowledge point

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These values are very close to each other, which is consistent with the visual estimate in part c that they are approximately the same.

Answer:

Question c

• A. The West store appears to have a greater mean since its histogram is centered further to the right than the East store's histogram is.
• B. The East store appears to have a greater mean since its histogram is centered further to the right than the West store's histogram is.</mcq-correct>
• C. The stores appear to have approximately the same mean since both histograms are centered around the same point. (Correct answer)

<mcq-option>D. It is impossible to make an inference about the means from the histograms alone.

Question d

• A. The West store appears to have a greater standard deviation since its histogram is wider than the East store's histogram is.
• B. The East store appears to have a greater standard deviation since its histogram is wider than the West store's histogram is. (Correct answer)
• C. The stores appear to have approximately the same standard deviation since both histograms have the same width.
• D. It is impossible to make an inference about the standard deviations from the histograms alone.

Question e

The mean for the East store is <blank>38.96</blank> and the mean for the West store is <blank>39.76</blank>. These values <blank>are</blank> consistent with the answer in part c.