Question

a machine dispensed red gumdrops into bags of various sizes. use the data to complete the histogram below. red gumdrops per bag 8 92 10 94 15 99 22 24 31 36 40 47 50 55 73 74 85 click to set the height of the missing bar. histogram with number of bags on x - axis (0 - 5) and number of red gumdrops on y - axis (1 - 20, 21 - 40, 41 - 60, 61 - 80, 81 - 100)

Explanation:

Step1: Identify the interval for the missing bar

The missing bar is for the interval 1 - 20 red gumdrops per bag. We need to count how many data points (red gumdrops per bag values) fall into this interval.
The data values are: 8, 10, 15, 22, 24, 31, 36, 40, 47, 50, 55, 73, 74, 85, 92, 94, 99.
Now, identify which of these are in 1 - 20: 8, 10, 15. So that's 3 values? Wait, no, wait. Wait, the x - axis of the histogram is "Number of bags" and the y - axis is "Number of red gumdrops" with intervals 1 - 20, 21 - 40, 41 - 60, 61 - 80, 81 - 100. Wait, maybe I misread. Wait, the y - axis is "Number of red gumdrops" with intervals: 1 - 20, 21 - 40, 41 - 60, 61 - 80, 81 - 100. And the x - axis is "Number of bags" (the height of each bar is the number of bags with that range of red gumdrops).
So let's list the data points (red gumdrops per bag) and assign them to intervals:
- 1 - 20: 8, 10, 15 → count = 3? Wait, no, the data points are: 8, 10, 15, 22, 24, 31, 36, 40, 47, 50, 55, 73, 74, 85, 92, 94, 99. Wait, how many? Let's count: 8 (1 - 20), 10 (1 - 20), 15 (1 - 20), 22 (21 - 40), 24 (21 - 40), 31 (21 - 40), 36 (21 - 40), 40 (21 - 40), 47 (41 - 60), 50 (41 - 60), 55 (41 - 60), 73 (61 - 80), 74 (61 - 80), 85 (81 - 100), 92 (81 - 100), 94 (81 - 100), 99 (81 - 100). Wait, that's 17 data points? Wait, no, the original data list: let's count the numbers. The left - hand side has: 8, 10, 15, 22, 24, 31, 36, 40, 47, 50, 55, 73, 74, 85, 92, 94, 99. Wait, that's 17 numbers? Wait, maybe I miscounted. Wait, 8,10,15 (3 numbers in 1 - 20), 22,24,31,36,40 (5 numbers in 21 - 40), 47,50,55 (3 numbers in 41 - 60), 73,74 (2 numbers in 61 - 80), 85,92,94,99 (4 numbers in 81 - 100). Wait, 3 + 5+3 + 2+4 = 17. Now, looking at the histogram:
- The bar for 21 - 40 has height 5 (since 5 numbers), which matches the purple bar (height 5).
- The bar for 41 - 60: 3 numbers? Wait, no, the orange bar for 41 - 60: let's see the x - axis (number of bags) has 0 - 5. Wait, the x - axis is "Number of bags" (so the height of the bar is the number of bags). Wait, maybe I had it reversed. Oh! Wait, the x - axis is "Number of bags" (the horizontal axis) and the y - axis is "Number of red gumdrops" (the vertical axis with intervals). Wait, no, the labels: the bottom axis is "Number of bags" (so the bars are along the x - axis, and the height of each bar is the count of bags with that range of red gumdrops. Wait, the histogram is a bar graph where each bar represents a range of red gumdrops (y - axis intervals) and the height of the bar is the number of bags (x - axis). Wait, the x - axis is labeled "Number of bags" with scale 0 - 5, and the y - axis is "Number of red gumdrops" with intervals 1 - 20, 21 - 40, 41 - 60, 61 - 80, 81 - 100.
So let's re - analyze:
We need to find how many bags have red gumdrops in 1 - 20. The data points (red gumdrops per bag) that are in 1 - 20: 8, 10, 15. So that's 3 bags? Wait, but the x - axis goes up to 5. Wait, maybe I made a mistake in the data. Wait, the data list: 8, 10, 15, 22, 24, 31, 36, 40, 47, 50, 55, 73, 74, 85, 92, 94, 99. Wait, 8,10,15: 3 values. 22,24,31,36,40: 5 values (21 - 40). 47,50,55: 3 values (41 - 60). 73,74: 2 values (61 - 80). 85,92,94,99: 4 values (81 - 100). Now, looking at the histogram:
- The bar for 21 - 40 (purple) has height 5 (matches our count of 5).
- The bar for 41 - 60 (orange) has height 3? Wait, no, the orange bar for 41 - 60: in the graph, the height (number of bags) for 41 - 60 is 3? Wait, the x - axis is 0 - 5. Wait, the bar for 21 - 40 is at height 5 (correct, 5 bags). The bar for 41 - 60: let's see, the data for 41 - 60 is 47,50,55 → 3 bags. The bar for 61 - 80: 73,74 → 2 bags. The bar for 81 - 100: 85,92,94,99 → 4 bags. The missing bar is for 1 - 20. The data for 1 - 20 is 8,10,15 → 3 bags. Wait, but the x - axis has 0 - 5. Wait, maybe I miscounted the data. Wait, let's list all the data points again: 8, 10, 15, 22, 24, 31, 36, 40, 47, 50, 55, 73, 74, 85, 92, 94, 99. Wait, that's 17 data points. 3 (1 - 20) + 5 (21 - 40)+3 (41 - 60)+2 (61 - 80)+4 (81 - 100)=3 + 5+3 + 2+4 = 17. Now, looking at the histogram:
- The bar for 21 - 40 (purple) is at height 5 (correct).
- The bar for 41 - 60 (orange) is at height 3? Wait, no, the orange bar for 41 - 60: in the graph, the height (number of bags) for 41 - 60 is 3? Wait, the x - axis is "Number of bags" with scale 0 - 5. So the bar for 1 - 20 should have a height equal to the number of bags with red gumdrops in 1 - 20. The data points in 1 - 20 are 8, 10, 15 → 3 bags. Wait, but maybe I made a mistake. Wait, 8,10,15: that's 3 values. So the height of the missing bar (for 1 - 20) should be 3? Wait, but let's check again. Wait, the data: 8 (1 - 20), 10 (1 - 20), 15 (1 - 20), 22 (21 - 40), 24 (21 - 40), 31 (21 - 40), 36 (21 - 40), 40 (21 - 40), 47 (41 - 60), 50 (41 - 60), 55 (41 - 60), 73 (61 - 80), 74 (61 - 80), 85 (81 - 100), 92 (81 - 100), 94 (81 - 100), 99 (81 - 100). Yes, that's 17 data points. So 3 in 1 - 20, 5 in 21 - 40, 3 in 41 - 60, 2 in 61 - 80, 4 in 81 - 100. So the missing bar (for 1 - 20) should have a height of 3 (number of bags). Wait, but the x - axis is 0 - 5, so the bar for 1 - 20 should reach up to 3 on the x - axis.

Step2: Confirm the count

Re - list the data points and their intervals:
- 1 - 20: 8, 10, 15 → count = 3
- 21 - 40: 22, 24, 31, 36, 40 → count = 5
- 41 - 60: 47, 50, 55 → count = 3
- 61 - 80: 73, 74 → count = 2
- 81 - 100: 85, 92, 94, 99 → count = 4

Now, looking at the histogram, the bar for 21 - 40 has height 5 (matches), 41 - 60 has height 3? Wait, no, the orange bar for 41 - 60: in the graph, the height (number of bags) for 41 - 60 is 3? Wait, the x - axis is "Number of bags" with scale 0 - 5. So the bar for 1 - 20 should have a height of 3 (since there are 3 bags with red gumdrops in 1 - 20).

Answer:

The height of the missing bar (for the 1 - 20 interval) should be 3 (since there are 3 bags with red gumdrops in the range 1 - 20). So on the histogram, the bar for 1 - 20 should reach up to 3 on the "Number of bags" (x - axis) scale.