Question

question 3 (1 point) for the histogram below, which data set represents the distribution of data for the number of pages in the last book read by each of 20 students over the summer?
histogram image with x-axis: number of pages (150, 200, 250, 300, 350, 400, 450) and y-axis (0-6)

a 163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431
b 150, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431
c 150, 170, 171, 173, 175, 205, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 431
d 163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 291, 305, 305, 306, 355, 388, 402, 431, 450

Explanation:

Step1: Count total data points

We need 20 data points (since there are 20 students). Let's check each option:

• Option a: Count the numbers. Let's list them: 163,170,171,173,175,205,220,220,220,253,267,281,305,305,305,355,371,388,402,431. Wait, that's 20? Wait, no, let's count again. Wait, 1 (163) + 4 (170,171,173,175) +1 (205)+3 (220s)+1 (253)+1 (267)+1 (281)+3 (305s)+1 (355)+1 (371)+1 (388)+1 (402)+1 (431). Wait, no, maybe better to count the number of elements. Let's count: 163 (1), 170 (2), 171 (3), 173 (4), 175 (5), 205 (6), 220 (7), 220 (8), 220 (9), 253 (10), 267 (11), 281 (12), 305 (13), 305 (14), 305 (15), 355 (16), 371 (17), 388 (18), 402 (19), 431 (20). Wait, that's 20? Wait, no, maybe I miscounted. Wait, let's check option c: 150,170,171,173,175,205,205,220,220,220,253,267,281,305,305,305,355,371,388,431. Wait, that's 20? Wait, no, let's check the histogram's bar heights. The first bar (150 - 200) has height 5, so 5 data points between 150 - 200. Second bar (200 - 250) has height 4, so 4 data points. Third (250 - 300): 3, fourth (300 - 350):3, fifth (350 - 400):3, sixth (400 - 450):2. Let's calculate total: 5+4+3+3+3+2 = 20. Good. Now check each option's data points in each interval.

Interval 1: 150 - 200 (inclusive? Or 150 ≤ x < 200? Let's assume 150 ≤ x < 200. So numbers from 150 to 199.

Option a: Data in 150-200: 163,170,171,173,175. That's 5? Wait, 163,170,171,173,175: 5 numbers. Wait, 163 is between 150-200, 170,171,173,175: total 5. Good.

Option b: Data in 150-200: 150,171,173,175. That's 4. Not 5. Eliminate b.

Option c: Data in 150-200: 150,170,171,173,175. That's 5. Good.

Option d: Data in 150-200: 163,170,171,173,175. 5. Good.

Interval 2: 200 - 250 (200 ≤ x < 250). Number of data points: 4.

Option a: Data in 200-250: 205,220,220,220. That's 4? Wait, 205, 220 (three times). Wait, 205 (1), 220 (3): total 4. Good.

Option c: Data in 200-250: 205,205,220,220,220. Wait, 205 (two times), 220 (three times): total 5. Which is more than 4. Eliminate c.

Option d: Data in 200-250: 205,220,220,220. 4. Good.

Interval 3: 250 - 300 (250 ≤ x < 300). Number of data points: 3.

Option a: Data in 250-300: 253,267,281. 3. Good.

Option d: Data in 250-300: 253,267,291. 3. Good.

Interval 4: 300 - 350 (300 ≤ x < 350). Number of data points: 3.

Option a: Data in 300-350: 305,305,305. 3. Good.

Option d: Data in 300-350: 305,305,306. 3. Good.

Interval 5: 350 - 400 (350 ≤ x < 400). Number of data points: 3.

Option a: Data in 350-400: 355,371,388. 3. Good.

Option d: Data in 350-400: 355,388. Wait, 355,388: that's 2. Wait, no, let's check d's data: 163,170,171,173,175,205,220,220,220,253,267,291,305,305,306,355,388,402,431,450. Wait, in 350-400: 355,388. Wait, that's 2. But we need 3. So option d has only 2 here. Eliminate d.

Interval 6: 400 - 450 (400 ≤ x < 450). Number of data points: 2.

Option a: Data in 400-450: 402,431. 2. Perfect.

Let's confirm option a:

• 150-200: 163,170,171,173,175 (5)
• 200-250: 205,220,220,220 (4)
• 250-300: 253,267,281 (3)
• 300-350: 305,305,305 (3)
• 350-400: 355,371,388 (3)
• 400-450: 402,431 (2)

Total: 5+4+3+3+3+2 = 20. Perfect.

Option c had 5 in 200-250, option d had 2 in 350-400, option b had 4 in 150-200. So only option a matches.

Answer:

a. 163, 170, 171, 173, 175, 205, 220, 220, 220, 253, 267, 281, 305, 305, 305, 355, 371, 388, 402, 431