Histograms Practice Worksheet

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 x-axis represents age ranges: \(0-9\), \(10-19\), \(20-29\), \(30-39\), \(40+\).
- The y-axis represents frequency (number of people).

From the histogram:
- \(0-9\): Frequency = 3
- \(10-19\): Frequency = 5
- \(20-29\): Frequency = 7
- \(30-39\): Frequency = 6
- \(40+\): Frequency = 4

Questions:

1. How many people were 20 years or older?
- People in the ranges \(20-29\), \(30-39\), and \(40+\):
\[
7 + 6 + 4 = 17
\]
- Answer: \(17\)

2. How many people were surveyed?
- Total frequency across all age ranges:
\[
3 + 5 + 7 + 6 + 4 = 25
\]
- Answer: \(25\)

3. What percentage of people were under 10?
- Number of people under 10: \(3\)
- Total number of people: \(25\)
- Percentage:
\[
\left( \frac{3}{25} \right) \times 100 = 12\%
\]
- Answer: \(12\%\)

4. What percentage of people were between 20 and 39?
- Number of people in the ranges \(20-29\) and \(30-39\):
\[
7 + 6 = 13
\]
- Total number of people: \(25\)
- Percentage:
\[
\left( \frac{13}{25} \right) \times 100 = 52\%
\]
- Answer: \(52\%\)

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 sum these products and 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 the midpoint of this open-ended range)
- Calculation:
\[
\text{Mean} = \frac{(4.5 \times 3) + (14.5 \times 5) + (24.5 \times 7) + (34.5 \times 6) + (45 \times 4)}{25}
\]
\[
= \frac{(13.5) + (72.5) + (171.5) + (207) + (180)}{25}
\]
\[
= \frac{644.5}{25} = 25.78
\]
- Answer: \(25.78\) (approximately \(26\))

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#### Section 2: Histogram of Car Ages

Histogram Description:
- The x-axis represents car age ranges: \(0-2\), \(3-4\), \(5-6\), \(7-8\), \(9+\).
- The y-axis represents frequency (number of households).

From the histogram:
- \(0-2\): Frequency = 20
- \(3-4\): Frequency = 30
- \(5-6\): Frequency = 40
- \(7-8\): Frequency = 50
- \(9+\): Frequency = 40

Questions:

6. How many households were surveyed?
- Total frequency across all car age ranges:
\[
20 + 30 + 40 + 50 + 40 = 180
\]
- Answer: \(180\)

7. What percentage of households had cars that are older than 7 years?
- Number of households with cars older than 7 years:
\[
50 + 40 = 90
\]
- Total number of households: \(180\)
- Percentage:
\[
\left( \frac{90}{180} \right) \times 100 = 50\%
\]
- Answer: \(50\%\)

8. What percentage of households have cars that are 5 years or older?
- Number of households with cars 5 years or older:
\[
40 + 50 + 40 = 130
\]
- Total number of households: \(180\)
- Percentage:
\[
\left( \frac{130}{180} \right) \times 100 \approx 72.22\%
\]
- Answer: \(72.22\%\)

9. How many households had cars between 3 and 8 years old?
- Number of households in the ranges \(3-4\), \(5-6\), and \(7-8\):
\[
30 + 40 + 50 = 120
\]
- Answer: \(120\)

10. Most households had cars in which range?
- The highest frequency is in the \(7-8\) range, with a frequency of \(50\).
- Answer: \(7-8\)

11. How many households have cars that are 4 years or less?
- Number of households in the ranges \(0-2\) and \(3-4\):
\[
20 + 30 = 50
\]
- Answer: \(50\)

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

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

Steps to Create the Histogram:

1. Determine the Range and Class Intervals:
- Minimum height: \(58\)
- Maximum height: \(74\)
- Class intervals: \(58-60\), \(61-63\), \(64-66\), \(67-69\), \(70+\)

2. Count Frequencies:
- \(58-60\): \(58, 60\) → Frequency = 2
- \(61-63\): \(62, 63, 63\) → Frequency = 3
- \(64-66\): \(65, 65, 66\) → Frequency = 3
- \(67-69\): \(68, 68\) → Frequency = 2
- \(70+\): \(70, 72, 74\) → Frequency = 3

3. Plot the Histogram:
- Draw the x-axis with class intervals.
- Draw the y-axis with frequencies.
- Plot the bars for each class interval with the corresponding frequency.

Final Answer for Section 3:
- The histogram will have the following frequencies:
- \(58-60\): 2
- \(61-63\): 3
- \(64-66\): 3
- \(67-69\): 2
- \(70+\): 3

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Final Answers:

1. \(17\)
2. \(25\)
3. \(12\%\)
4. \(52\%\)
5. \(25.78\)
6. \(180\)
7. \(50\%\)
8. \(72.22\%\)
9. \(120\)
10. \(7-8\)
11. \(50\)
12. Histogram with frequencies: \(58-60: 2\), \(61-63: 3\), \(64-66: 3\), \(67-69: 2\), \(70+: 3\)

\(\boxed{25.78}\) (for Question 5)