Histograms Practice Worksheet with age, car age, and height data for educational use.

Problem Analysis and Solution

The image contains three sections with tasks related to histograms. Let's solve each section step by step.

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#### Section 1: Histogram of Ages

Histogram Description:
- The histogram shows the frequency of people entering a mall, grouped into age ranges: 0-9, 10-19, 20-29, 30-39, and 40+.
- The frequencies for each age range are as follows (estimated from the histogram):
- 0-9: 3
- 10-19: 5
- 20-29: 7
- 30-39: 4
- 40+: 2

Questions:

1. How many people were 20 years or older?
- People in the age ranges 20-29, 30-39, and 40+:
- 20-29: 7
- 30-39: 4
- 40+: 2
- Total: \( 7 + 4 + 2 = 13 \)
- Answer: 13

2. How many people were surveyed?
- Sum of all frequencies:
- 0-9: 3
- 10-19: 5
- 20-29: 7
- 30-39: 4
- 40+: 2
- Total: \( 3 + 5 + 7 + 4 + 2 = 21 \)
- Answer: 21

3. What percentage of people were under 10?
- Number of people under 10: 3
- Total number of people surveyed: 21
- Percentage: \( \frac{3}{21} \times 100 \approx 14.29\% \)
- Answer: 14.29%

4. What percentage of people were between 20 and 39?
- Number of people between 20 and 39:
- 20-29: 7
- 30-39: 4
- Total: \( 7 + 4 = 11 \)
- Total number of people surveyed: 21
- Percentage: \( \frac{11}{21} \times 100 \approx 52.38\% \)
- Answer: 52.38%

5. Estimate the mean age of the people surveyed.
- To estimate the mean, we use the midpoint of each age range and multiply it by the frequency, then divide by the total number of people.
- Midpoints:
- 0-9: 4.5
- 10-19: 14.5
- 20-29: 24.5
- 30-39: 34.5
- 40+: 45 (assuming an average of 45 for simplicity)
- Calculation:
\[
\text{Mean} = \frac{(4.5 \times 3) + (14.5 \times 5) + (24.5 \times 7) + (34.5 \times 4) + (45 \times 2)}{21}
\]
\[
= \frac{(13.5) + (72.5) + (171.5) + (138) + (90)}{21}
\]
\[
= \frac{585.5}{21} \approx 27.88
\]
- Answer: 27.88

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#### Section 2: Histogram of Car Ages

Histogram Description:
- The histogram shows the frequency of households based on the age of their primary vehicle in years: 0-2, 3-4, 5-6, 7-8, and 9+.
- The frequencies for each car age range are as follows (estimated from the histogram):
- 0-2: 10
- 3-4: 20
- 5-6: 40
- 7-8: 60
- 9+: 70

Questions:

6. How many households were surveyed?
- Sum of all frequencies:
- 0-2: 10
- 3-4: 20
- 5-6: 40
- 7-8: 60
- 9+: 70
- Total: \( 10 + 20 + 40 + 60 + 70 = 200 \)
- Answer: 200

7. What percentage of households had cars that are older than 7 years?
- Number of households with cars older than 7 years:
- 7-8: 60
- 9+: 70
- Total: \( 60 + 70 = 130 \)
- Total number of households surveyed: 200
- Percentage: \( \frac{130}{200} \times 100 = 65\% \)
- Answer: 65%

8. What percentage of households have cars that are 5 years or older?
- Number of households with cars 5 years or older:
- 5-6: 40
- 7-8: 60
- 9+: 70
- Total: \( 40 + 60 + 70 = 170 \)
- Total number of households surveyed: 200
- Percentage: \( \frac{170}{200} \times 100 = 85\% \)
- Answer: 85%

9. How many households had cars between 3 and 8 years old?
- Number of households with cars between 3 and 8 years old:
- 3-4: 20
- 5-6: 40
- 7-8: 60
- Total: \( 20 + 40 + 60 = 120 \)
- Answer: 120

10. Most households had cars in which range?
- The highest frequency is in the 9+ range (70 households).
- Answer: 9+

11. How many households have cars that are 4 years or less?
- Number of households with cars 4 years or less:
- 0-2: 10
- 3-4: 20
- Total: \( 10 + 20 = 30 \)
- Answer: 30

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#### Section 3: Creating a Histogram for Heights

Data:
- Heights in inches: 60", 58", 63", 65", 72", 68", 74", 63", 68", 62", 66", 70", 65"

Task:
- Create a histogram using the provided data and the given bins: 58-60, 61-63, 64-66, 67-69, 70+.

Solution:
1. Count the frequencies for each bin:
- 58-60: 2 (58, 60)
- 61-63: 3 (61, 62, 63)
- 64-66: 3 (64, 65, 65)
- 67-69: 3 (67, 68, 68)
- 70+: 4 (70, 72, 74)

2. Plot the histogram:
- The x-axis represents the height ranges (bins).
- The y-axis represents the frequency.
- Frequencies:
- 58-60: 2
- 61-63: 3
- 64-66: 3
- 67-69: 3
- 70+: 4

Answer: The histogram is created with the above frequencies.

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Final Answers:

1. 13
2. 21
3. 14.29%
4. 52.38%
5. 27.88
6. 200
7. 65%
8. 85%
9. 120
10. 9+
11. 30
12. Histogram created with frequencies: 58-60 (2), 61-63 (3), 64-66 (3), 67-69 (3), 70+ (4).

Boxed Final Answer:
\[
\boxed{13, 21, 14.29\%, 52.38\%, 27.88, 200, 65\%, 85\%, 120, 9+, 30}
\]