Find the mean for the data items in the given frequency distribution. 3 1 Score, x Frequency, f The mean is 1 1 2 2 4 6 5 5 (Round to 3 decimal places as needed.) 6 9 7 5 38 9 3 10 3
Find the mean for the data items in the given frequency distribution. 3 1 Score, x Frequency, f The mean is 1 1 2 2 4 6 5 5 (Round to 3 decimal places as needed.) 6 9 7 5 38 9 3 10 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
21: Answer
![**Finding the Mean of a Frequency Distribution**
To find the mean for the data items in the given frequency distribution, follow the steps below:
**Frequency Distribution Table:**
| Score (x) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|-----------|---|---|---|---|---|---|---|---|---|----|
| Frequency (f) | 1 | 2 | 1 | 6 | 5 | 9 | 5 | 3 | 3 | 3 |
**Steps to Calculate the Mean:**
1. **Multiply each score (x) by its frequency (f) to get the total for each value.**
Total = \( x \times f \)
2. **Sum all the totals from Step 1** to find the sum of all the value-frequency products.
3. **Sum all the frequencies** to find the total number of data items.
4. **Divide the total from Step 2 by the total frequency from Step 3** to get the mean.
**Example:**
- For Score 1: Total = \( 1 \times 1 = 1 \)
- For Score 2: Total = \( 2 \times 2 = 4 \)
- Repeat this process for all scores.
**Finally:**
- Calculate the mean using the formula:
\[
\text{Mean} = \frac{\sum (x \times f)}{\sum f}
\]
**Round the result to 3 decimal places as needed.**
**Solution Placeholder:**
The mean is \[ \_\_\_\_\_ \]
Complete the calculations to find the mean accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8470e22-cdb6-4814-babe-099f6875e962%2Ff91dbc6a-7001-48f4-8b4e-af4f303ce369%2Fuo4wiq8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Mean of a Frequency Distribution**
To find the mean for the data items in the given frequency distribution, follow the steps below:
**Frequency Distribution Table:**
| Score (x) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|-----------|---|---|---|---|---|---|---|---|---|----|
| Frequency (f) | 1 | 2 | 1 | 6 | 5 | 9 | 5 | 3 | 3 | 3 |
**Steps to Calculate the Mean:**
1. **Multiply each score (x) by its frequency (f) to get the total for each value.**
Total = \( x \times f \)
2. **Sum all the totals from Step 1** to find the sum of all the value-frequency products.
3. **Sum all the frequencies** to find the total number of data items.
4. **Divide the total from Step 2 by the total frequency from Step 3** to get the mean.
**Example:**
- For Score 1: Total = \( 1 \times 1 = 1 \)
- For Score 2: Total = \( 2 \times 2 = 4 \)
- Repeat this process for all scores.
**Finally:**
- Calculate the mean using the formula:
\[
\text{Mean} = \frac{\sum (x \times f)}{\sum f}
\]
**Round the result to 3 decimal places as needed.**
**Solution Placeholder:**
The mean is \[ \_\_\_\_\_ \]
Complete the calculations to find the mean accurately.
Expert Solution
Step 1
The data for the frequency distribution is given by :
| Score, x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| frequency, f | 1 | 2 | 1 | 6 | 5 | 9 | 5 | 3 | 3 | 3 |
we have to find the mean for the given data.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
