A set of 30 people were asked how many coins they had in thier pockets and the following results were obtained : No. Of Coins = 0-4, 5-7, 8-10, 11-12. No. Of people = 6, 8, 8, 8. Find the mean of the coins.
To find the mean number of coins, you’ll need to calculate the weighted average based on the number of people in each group. Here’s how you can do it:
- Multiply the midpoints of each group by the number of people in that group.
- Sum up the products from step 1.
- Divide the sum from step 2 by the total number of people.
Given data:
| No. of coins | No. of people |
|---|---|
| 0-4 | 6 |
| 5-7 | 8 |
| 8-10 | 8 |
| 11-12 | 8 |
Calculations:
- Calculate the midpoints of the ranges:
- Midpoint of 0-4: (0 + 4) / 2 = 2
- Midpoint of 5-7: (5 + 7) / 2 = 6
- Midpoint of 8-10: (8 + 10) / 2 = 9
- Midpoint of 11-12: (11 + 12) / 2 = 11.5
- Multiply the midpoints by the number of people in each group:
- (2 * 6) + (6 * 8) + (9 * 8) + (11.5 * 8) = 252
- Divide the sum by the total number of people: 252 / 30 = 8.4
The mean number of coins is 8.4.
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More Similar Examples
Example 2: A study recorded the number of hours 50 students studied for an exam. The data is given below:
| Study Hours | No. of Students |
|---|---|
| 0-2 | 5 |
| 3-5 | 10 |
| 6-8 | 15 |
| 9-10 | 20 |
Calculate the mean study hours.
Solution:
- Calculate the midpoints:
- Midpoint of 0-2: (0 + 2) / 2 = 1
- Midpoint of 3-5: (3 + 5) / 2 = 4
- Midpoint of 6-8: (6 + 8) / 2 = 7
- Midpoint of 9-10: (9 + 10) / 2 = 9.5
- Multiply the midpoints by the number of students in each group:
- (1 * 5) + (4 * 10) + (7 * 15) + (9.5 * 20) = 342.5
- Divide the sum by the total number of students: 342.5 / 50 = 6.85
The mean study hours is 6.85.
Example 3: A survey gathered data on the monthly expenses of 60 households. The data is as follows:
| Expenses (in $) | No. of Households |
|---|---|
| 0-200 | 10 |
| 201-400 | 18 |
| 401-600 | 20 |
| 601-800 | 12 |
Calculate the mean monthly expenses.
Solution:
- Calculate the midpoints:
- Midpoint of 0-200: (0 + 200) / 2 = 100
- Midpoint of 201-400: (201 + 400) / 2 = 300.5
- Midpoint of 401-600: (401 + 600) / 2 = 500.5
- Midpoint of 601-800: (601 + 800) / 2 = 700.5
- Multiply the midpoints by the number of households in each group:
- (100 * 10) + (300.5 * 18) + (500.5 * 20) + (700.5 * 12) = 23845.5
- Divide the sum by the total number of households: 23845.5 / 60 ≈ 397.425
The mean monthly expenses are approximately $397.43.
[mediator_tech]
Example 4: A group of 25 students were surveyed about their daily screen time (in minutes). The data is given below:
| Screen Time (in min) | No. of Students |
|---|---|
| 0-30 | 5 |
| 31-60 | 8 |
| 61-90 | 7 |
| 91-120 | 5 |
Calculate the mean screen time.
Solution:
- Calculate the midpoints:
- Midpoint of 0-30: (0 + 30) / 2 = 15
- Midpoint of 31-60: (31 + 60) / 2 = 45.5
- Midpoint of 61-90: (61 + 90) / 2 = 75.5
- Midpoint of 91-120: (91 + 120) / 2 = 105.5
- Multiply the midpoints by the number of students in each group:
- (15 * 5) + (45.5 * 8) + (75.5 * 7) + (105.5 * 5) = 2845
- Divide the sum by the total number of students: 2845 / 25 = 113.8
The mean screen time is 113.8 minutes.
Evaluation
1. A survey collected data on the ages of participants. The results are as follows:
| Age Group | No. of Participants |
|---|---|
| 0-10 | 5 |
| 11-20 | 8 |
| 21-30 | 10 |
| 31-40 | 7 |
Calculate the mean age.
a) 25.75
b) 20.75
c) 19.5
2. A study recorded the scores of 60 students in a test. The data is given below:
| Test Score | No. of Students |
|---|---|
| 0-20 | 6 |
| 21-40 | 12 |
| 41-60 | 18 |
| 61-80 | 24 |
Calculate the mean test score.
a) 57.5
b) 55.2
c) 50.9
3. A survey collected data on the heights of individuals. The results are as follows:
| Height Range (in inches) | No. of Individuals |
|---|---|
| 50-60 | 10 |
| 61-70 | 15 |
| 71-80 | 12 |
| 81-90 | 8 |
Calculate the mean height.
a) 66.6
b) 67.3
c) 68.2
4. A study recorded the number of items sold by 40 vendors. The data is given below:
| Items Sold | No. of Vendors |
|---|---|
| 0-5 | 7 |
| 6-10 | 12 |
| 11-15 | 10 |
| 16-20 | 11 |
Calculate the mean number of items sold.
a) 9.2
b) 9.8
c) 10.4
[mediator_tech]
5. A survey gathered data on the ages of 50 participants. The results are as follows:
| Age Group | No. of Participants |
|---|---|
| 0-18 | 12 |
| 19-30 | 15 |
| 31-50 | 13 |
| 51-70 | 10 |
Calculate the mean age.
a) 31.6
b) 33.2
c) 35.4
6. A study recorded the temperatures in degrees Celsius for 70 days. The data is given below:
| Temperature | No. of Days |
|---|---|
| 0-10 | 15 |
| 11-20 | 18 |
| 21-30 | 20 |
| 31-40 | 17 |
Calculate the mean temperature.
a) 22.7
b) 23.5
c) 24.9
7. A survey collected data on the number of pets owned by individuals. The results are as follows:
| No. of Pets | No. of Individuals |
|---|---|
| 0-2 | 8 |
| 3-5 | 12 |
| 6-8 | 15 |
| 9-10 | 10 |
Calculate the mean number of pets.
a) 5.1
b) 4.8
c) 4.4
8. A study recorded the distance (in kilometers) traveled by 30 cyclists. The data is given below:
| Distance | No. of Cyclists |
|---|---|
| 0-5 | 6 |
| 6-10 | 10 |
| 11-15 | 8 |
| 16-20 | 6 |
Calculate the mean distance.
a) 8.6
b) 9.2
c) 9.8
9. A survey collected data on the income (in thousands) of individuals. The results are as follows:
| Income | No. of Individuals |
|---|---|
| 0-10 | 5 |
| 11-20 | 8 |
| 21-30 | 7 |
| 31-40 | 10 |
Calculate the mean income.
a) 27.6
b) 28.3
c) 29.9
10. A study recorded the weights (in pounds) of 25 individuals. The data is given below:
| Weight | No. of Individuals |
|---|---|
| 0-50 | 5 |
| 51-100 | 7 |
| 101-150 | 8 |
| 151-200 | 5 |
Calculate the mean weight.
a) 110.4
b) 111.8
c) 113.2
Definitions:
- Qualitative Data: Qualitative data are non-numerical observations, often categorized into groups based on characteristics or attributes. Examples include gender, color, or type of car.
- Descriptive Statistics: Descriptive statistics involve methods used to summarize and describe data. They include measures like mean, median, mode, and standard deviation.
- Parametric Statistics: Parametric statistics are methods used when data follow specific distributions and assumptions. They require data to be measured on an interval or ratio scale. Examples include t-tests and ANOVA.
1. Qualitative data refers to non-_____ observations that are categorized based on attributes or characteristics.
a) Categorical
b) Numerical
c) Descriptive
2. Descriptive statistics involve methods used to ________ and describe data.
a) Predict
b) Summarize
c) Analyze
3. Parametric statistics are used when data follow specific distributions and assumptions, requiring measurements on an interval or ______ scale.
a) Nominal
b) Ordinal
c) Ratio
4. A researcher is analyzing survey responses categorized by the type of music preferred by participants. This data is an example of ________.
a) Descriptive statistics
b) Parametric statistics
c) Qualitative data
5. The ______ scale of measurement involves categories that have no meaningful order.
a) Ratio
b) Ordinal
c) Nominal
6. When data can be ranked, but the intervals between values are not consistent, the scale of measurement is ______.
a) Nominal
b) Ratio
c) Ordinal
7. A researcher measures the height of individuals in centimeters. This is an example of ______ data.
a) Qualitative
b) Categorical
c) Numerical
8. A sample of 50 people rated their satisfaction level on a scale of 1 to 5. This data is an example of ______ data.
a) Qualitative
b) Nominal
c) Ordinal
9. Parametric statistics often assume that the data follows a ______ distribution.
a) Normal
b) Exponential
c) Uniform
10. Descriptive statistics aim to provide a ______ summary of data.
a) Detailed
b) Statistical
c) Concise
11. Parametric statistics require data to be measured on a(n) ______ scale.
a) Ordinal
b) Interval
c) Nominal
12. A researcher calculates the mean of a dataset. This is an example of ______ statistics.
a) Descriptive
b) Inferential
c) Parametric
13. When data can be ordered and the intervals are meaningful, but the ratio between values is not, the scale of measurement is ______.
a) Ordinal
b) Interval
c) Ratio
14. A survey records the colors of cars owned by participants. This data is an example of ______.
a) Parametric statistics
b) Qualitative data
c) Descriptive statistics
15. The ______ scale of measurement has categories with a meaningful order and consistent intervals.
a) Nominal
b) Interval
c) Ordinal