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

b) draw a histogram indicating the number of oil changes at each store.

choose the histogram for the east store below.
choose the histogram for the west store below.

Explanation:

Analyze the East Store data

Using the Histogram Interpretation knowledge point
Let's count the frequencies of the East Store data using standard class intervals of width 10 starting from 10:

• East Store data:

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

Let's group them into bins:

• \(10 \le x < 20\): 15 (1 value) -> Frequency = 1
• \(20 \le x < 30\): 27, 29, 20, 29, 25, 27 (6 values) -> Frequency = 6
• \(30 \le x < 40\): 37, 32, 37, 32, 38, 39, 37 (7 values) -> Frequency = 7
• \(40 \le x < 50\): 43, 44, 44, 46, 42, 46 (6 values) -> Frequency = 6
• \(50 \le x < 60\): 58, 54, 54, 51 (4 values) -> Frequency = 4
• \(60 \le x < 70\): 69 (1 value) -> Frequency = 1

Looking at the options for the East store:

• Option B shows:
• Bin 10–20: height 1
• Bin 20–30: height 6
• Bin 30–40: height 7
• Bin 40–50: height 6
• Bin 50–60: height 4
• Bin 60–70: height 1

Thus, Option B is correct for the East store.

Analyze the West Store data

Using the Histogram Interpretation knowledge point
Let's count the frequencies of the West Store data using the same class intervals:

• West Store data:

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

Let's group them into bins:

• \(10 \le x < 20\): None (0 values) -> Frequency = 0
• \(20 \le x < 30\): 28 (1 value) -> Frequency = 1
• \(30 \le x < 40\): 34, 37, 39, 32, 39, 36, 30, 37, 33, 36, 31 (11 values) -> Frequency = 11
• \(40 \le x < 50\): 42, 43, 43, 40, 42, 42, 41, 42, 48, 43, 49, 42, 46 (13 values) -> Frequency = 13
• \(50 \le x < 60\): None (0 values) -> Frequency = 0

Looking at the options for the West store:

• Option B shows:
• Bin 20–30: height 1
• Bin 30–40: height 11
• Bin 40–50: height 13

Thus, Option B is correct for the West store.

Answer:

Question 1

• A. Histogram with peak on the right side
• B. Histogram with frequencies: [10-20: 1, 20-30: 6, 30-40: 7, 40-50: 6, 50-60: 4, 60-70: 1] (Correct answer)
• C. Histogram with peak in the middle around 40
• D. Histogram skewed to the left with peak near 70

Question 2

• A. Histogram skewed to the left with peak near 60
• B. Histogram with frequencies: [20-30: 1, 30-40: 11, 40-50: 13] (Correct answer)
• C. Histogram with peak around 30-40
• D. Histogram skewed to the left with peak near 70