Question

at their family reunion, the blake family recorded everyone’s age. use the data to complete the histogram below. ages 1 6 8 9 10 14 16 26 32 40 46 click to set the height of the missing bar. (histogram with age groups 0 - 9, 10 - 19, 20 - 29, 30 - 39, 40 - 49 and number of people axis, some bars filled, 30 - 39 bar missing)

Explanation:

Step1: Identify the missing bar

The histogram has a missing bar for the age group 30 - 39. We need to determine the number of people in this age group from the given data.

Step2: Analyze the data

Looking at the left - hand side, the data points for ages are 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46. We need to count how many of these fall into the 30 - 39 age range. The values 32 and 40? Wait, no. Wait, 32 is in 30 - 39? Wait, 30 - 39 includes ages from 30 to 39. So 32 is in 30 - 39, and what about others? Wait, maybe I misread. Wait, the data is the ages of the family members. Let's list the ages: 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46. Now, the age group 30 - 39: which of these ages are in 30 - 39? 32 is in 30 - 39. Wait, is that all? Wait, maybe I made a mistake. Wait, maybe the data is the number of people? No, the left - hand side says "Ages" with values 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46. Wait, no, maybe those are the ages of the family members. So we need to count how many family members have ages between 30 and 39. Let's check each age:

- 1: 0 - 9
- 6: 0 - 9
- 8: 0 - 9
- 9: 0 - 9
- 10: 10 - 19
- 14: 10 - 19
- 16: 10 - 19
- 26: 20 - 29
- 32: 30 - 39
- 40: 40 - 49
- 46: 40 - 49

Wait, that's only one age (32) in 30 - 39? But that can't be. Wait, maybe the left - hand side is the number of people? Wait, the y - axis of the histogram is "Number of people" (wait, the label is reversed, "Number of people" is on the x - axis? No, the x - axis is "Number of people" (from 0 to 5) and the y - axis is "Age" with groups 0 - 9, 10 - 19, 20 - 29, 30 - 39, 40 - 49. Wait, I think I misread the axes. Let's re - orient:

The horizontal axis (x - axis) is "Number of people" (ranging from 0 to 5), and the vertical axis (y - axis) is "Age" with categories 0 - 9, 10 - 19, 20 - 29, 30 - 39, 40 - 49.

The bars:

- 0 - 9: the bar goes up to 4 on the x - axis (number of people)
- 10 - 19: the bar (purple) goes up to 3? Wait, no, the purple bar for 10 - 19: the x - axis (number of people) for 10 - 19 is 3? Wait, no, the x - axis is labeled "Number of people" with ticks 0, 1, 2, 3, 4, 5. The y - axis is "Age" with groups 0 - 9, 10 - 19, 20 - 29, 30 - 39, 40 - 49.

Wait, the 0 - 9 age group has a bar that reaches x = 4 (number of people).

The 10 - 19 age group (purple) reaches x = 3?

The 20 - 29 age group reaches x = 1?

The 40 - 49 age group reaches x = 2?

And the 30 - 39 age group is missing. Now, we need to find how many people are in the 30 - 39 age group from the given age data: 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46.

Let's count the number of people with age in 30 - 39:

- Age 32: 1 person
- Any others? 40 is in 40 - 49, 26 is in 20 - 29, 10,14,16 in 10 - 19, 1,6,8,9 in 0 - 9. Wait, that's only 1? But that seems odd. Wait, maybe the data is the number of people per age? No, the left - hand side is the list of ages. Wait, maybe I made a mistake. Wait, the problem says "Use the data to complete the histogram". The data is the ages of the family members: 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46.

Now, let's categorize each age into the age groups:

- 0 - 9: 1, 6, 8, 9 → 4 people (matches the 0 - 9 bar which is at x = 4)
- 10 - 19: 10, 14, 16 → 3 people (matches the 10 - 19 bar which is at x = 3)
- 20 - 29: 26 → 1 person (matches the 20 - 29 bar which is at x = 1)
- 30 - 39: 32 → 1 person? Wait, no, 32 is in 30 - 39, and is there another? 40 is in 40 - 49, 46 is in 40 - 49. Wait, so 32 is in 30 - 39, so the number of people in 30 - 39 is 1? But that seems too low. Wait, maybe I misread the data. Wait, the data is: 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46. Let's count again:

0 - 9: 1,6,8,9 → 4 (correct, bar at 4)

10 - 19:10,14,16 → 3 (correct, bar at 3)

20 - 29:26 → 1 (correct, bar at 1)

30 - 39:32 → 1? Wait, but 40 and 46 are in 40 - 49. Wait, 40 is 40, so 40 - 49: 40,46 → 2 people (correct, bar at 2)

So the 30 - 39 age group has 1 person? But that seems odd. Wait, maybe the data is different. Wait, maybe the left - hand side is the number of people, not the ages. Oh! That's probably my mistake. The left - hand side says "Ages" but maybe it's the number of people with each age? No, that doesn't make sense. Wait, no, the problem says "the Blake family recorded everyone's age" and "Use the data to complete the histogram". So the data is the list of ages: 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46. So we need to count how many are in each age group.

So for 30 - 39: ages between 30 and 39 (inclusive). So 32 is in 30 - 39. Is there any other? 40 is 40, which is in 40 - 49. So only 32, so the number of people in 30 - 39 is 1. Wait, but the x - axis of the histogram is "Number of people" from 0 to 5. So the bar for 30 - 39 should be at x = 1. But that seems too short. Wait, maybe I misread the age data. Let's check again: the ages are 1, 6, 8, 9, 10, 14, 16, 26, 32, 40, 46. So that's 11 ages? Wait, 1,6,8,9,10,14,16,26,32,40,46: that's 11 ages. Now, let's count the number of people in each group:

- 0 - 9: 1,6,8,9 → 4 (4 people)
- 10 - 19:10,14,16 → 3 (3 people)
- 20 - 29:26 → 1 (1 person)
- 30 - 39:32 → 1 (1 person)
- 40 - 49:40,46 → 2 (2 people)

4 + 3+1 + 1+2 = 11, which matches the number of ages. So the number of people in the 30 - 39 age group is 1. So the bar for 30 - 39 should be set to x = 1 (number of people = 1).

Answer:

The height of the missing bar (for 30 - 39 age group) should be set to 1 (corresponding to the number of people in that age group, which is 1).