Question

the architecture student counted the number of bricks in each building in her neighborhood. use the data to complete the histogram below. bricks per building: 1, 20; 2, 24; 3, 9; 4, 5; 5, 10; 6, 11; 7, 14; 8, 14; 9, 14; 10, 14; 11, 17; 12, 17; 13, 17; 14, 19. click to set the height of a missing bar. histogram with number of buildings on y - axis (0 - 5) and number of bricks on x - axis (1 - 5, 6 - 10, 11 - 15, 16 - 20, 21 - 25); bars for 1 - 5 (green), 6 - 10 (purple), 11 - 15 (green) are present, 16 - 20 and 21 - 25 are missing

Explanation:

Step1: Classify data into intervals

First, we categorize the number of bricks per building into the given intervals (1 - 5, 6 - 10, 11 - 15, 16 - 20, 21 - 25).
- For 1 - 5: The values are 1, 2, 3, 4, 5. Let's count them: 1 (1), 2 (2), 3 (3), 4 (4), 5 (5) – wait, no, looking at the data list: the numbers are 1, 2, 3, 4, 5, 9, 10, 11, 14, 14, 14, 14, 14, 17, 17, 19, 20, 24? Wait, maybe I misread. Wait the left data: Bricks per building: 1, 2, 3, 4, 5, 9, 10, 11, 14, 14, 14, 14, 14, 17, 17, 19, 20, 24? Wait no, the numbers given are: 1, 2, 3, 4, 5, 9, 10, 11, 14 (five times), 17 (two times), 19, 20, 24? Wait maybe the original data is: 1, 2, 3, 4, 5, 9, 10, 11, 14,14,14,14,14,17,17,19,20,24? Wait the histogram has intervals 1 - 5, 6 - 10, 11 - 15, 16 - 20, 21 - 25.

Let's count each interval:

- 1 - 5: numbers 1,2,3,4,5 → that's 5 values (wait 1,2,3,4,5: 5 numbers)
- 6 - 10: numbers 9,10 → wait no, 9 and 10? Wait 9,10, and is there 6,7,8? The data given: 5,9,10,11,... Wait the data list on the left: Bricks per building: 1, 2, 3, 4, 5, 9, 10, 11, 14,14,14,14,14,17,17,19,20,24? Wait maybe I miscounted. Wait the numbers are: 1, 2, 3, 4, 5, 9, 10, 11, 14 (five times: 14,14,14,14,14), 17 (two times:17,17), 19, 20, 24. Wait so:

1 - 5: 1,2,3,4,5 → 5 buildings (count: 5)
6 - 10: 9,10 → wait 9 and 10, and is there 6,7,8? No, so 9 and 10: that's 2? Wait no, 9 and 10: two numbers? Wait 9 and 10: so count is 2? But the histogram's 6 - 10 bar is purple, height? Wait the histogram on the right: 1 - 5: green bar, height 5 (since 1-5 has 5 values: 1,2,3,4,5). 6 - 10: numbers 9,10, and maybe 6,7,8? Wait no, the data given: 5,9,10,11,... Wait maybe the data is: 1,2,3,4,5 (1-5: 5), 6-10: 9,10 (wait 9 and 10, but also 6? No, the data has 5, then 9,10. So 6-10: 9,10, and maybe 6? No, the data list is: 1,2,3,4,5,9,10,11,14,14,14,14,14,17,17,19,20,24. Wait so 6-10: 9,10 (two numbers? But 9 and 10 are in 6-10 (since 6 ≤ x ≤10). So count is 2? But the purple bar in the histogram is at height 2? Wait no, the histogram's 6-10 bar: the y-axis is number of buildings. Wait the 1-5 bar is height 5 (since 1,2,3,4,5: 5 buildings). 6-10: numbers 9,10, and also 6? No, the data has 5, then 9,10. So 6-10: 9,10 (two) and maybe 6? No, the data given doesn't have 6,7,8. So 6-10: 9,10 (two) and 9,10: wait 9 and 10 are two numbers? Wait 9 and 10: that's two, but also 9 is 9, 10 is 10. Wait maybe I made a mistake. Wait the data list: let's list all numbers:

1, 2, 3, 4, 5, 9, 10, 11, 14, 14, 14, 14, 14, 17, 17, 19, 20, 24. Wait that's 18 numbers? Wait no, the left side: Bricks per building: 1, 2, 3, 4, 5, 9, 10, 11, 14,14,14,14,14,17,17,19,20,24? Wait 1 (1), 2 (2), 3 (3), 4 (4), 5 (5), 9 (6), 10 (7), 11 (8), 14 (9,10,11,12,13), 17 (14,15), 19 (16), 20 (17), 24 (18). So 18 buildings.

Now categorize:

- 1 - 5: 1,2,3,4,5 → 5 buildings (correct, as the green bar for 1-5 is height 5)
- 6 - 10: 9,10 → wait 9 and 10: that's 2? But 9 and 10 are in 6-10. Wait but also 6? No, data doesn't have 6,7,8. So 6-10: 9,10 (two) and 9,10: wait 9 is 9, 10 is 10. So two buildings? But the purple bar in the histogram is at height 2? Wait no, the purple bar is at height 2? Wait the histogram shows 6-10 bar at height 2? Wait no, maybe I misread the data. Wait the numbers: 5,9,10: wait 5 is in 1-5, 9 and 10 in 6-10. Then 11-15: 11,14,14,14,14,14 → 11, and five 14s: total 6 buildings (11 + 5*14: 6). 16-20: 17,17,19,20 → 17 (two), 19, 20: total 4 buildings (2+1+1=4). 21-25: 24 → 1 building.

Wait let's check:

1-5: 5 (1,2,3,4,5)
6-10: 9,10 (2)
11-15: 11,14,14,14,14,14 (6)
16-20: 17,17,19,20 (4)
21-25: 24 (1)

Now the histogram:

- 1-5: green bar, height 5 (matches)
- 6-10: purple bar, height 2 (matches if 9 and 10 are two)
- 11-15: green bar, height 6 (since 11 + five 14s: 6)
- 16-20: missing bar. Let's count 16-20: numbers 17,17,19,20. So that's 4 buildings. So the bar for 16-20 should have height 4.
- 21-25: 24, so height 1.

Wait the problem says "Click to set the height of a missing bar". The missing bar is probably 16-20. Let's confirm:

Data in 16-20: 17,17,19,20. So count is 4. So the bar for 16-20 should be at height 4 (since the y-axis is number of buildings, with 0,1,2,3,4,5). So the missing bar (16-20) should have height 4.

Step2: Determine the missing bar height

The interval 16 - 20 includes the values 17, 17, 19, 20. Counting these, we get 4 values. So the height of the bar for 16 - 20 should be 4 (since each unit on the y-axis represents one building, and the y-axis goes from 0 to 5).

Answer:

The height of the missing bar (for 16 - 20 bricks) is 4. So we set the bar to height 4.