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.

Explanation:

Analyze the histograms for center

Using the Histogram Interpretation and Mean Calculation knowledge points

• The East Store histogram has its data centered around the interval \(30\text{--}50\).
• The West Store histogram is also centered around the interval \(30\text{--}50\).
• Both distributions are roughly symmetric and centered around the same region (approximately \(40\)).
• Therefore, the stores appear to have approximately the same mean.

Analyze the histograms for spread

Using the Histogram Interpretation and Standard Deviation knowledge points

• The East Store histogram has data values spanning from \(10\) to \(70\).
• The West Store histogram has data values spanning from \(20\) to \(60\).
• The East Store's histogram is wider (more spread out) than the West Store's histogram.
• A wider distribution indicates a larger standard deviation.
• Therefore, the East Store appears to have a greater standard deviation.

Answer:

Question 1

• (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.
• (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.
• (C) The stores appear to have approximately the same mean since both histograms are centered around the same point. (Correct answer)
• (D) It is impossible to make an inference about the means from the histograms alone.

Question 2

• (A) The West store appears to have a greater standard deviation since its histogram is wider than the East store's histogram.
• (B) The East store appears to have a greater standard deviation since its histogram is wider than the West store's histogram. (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.