MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Understanding Median in Frequency Distribution**
To find the median of given data within a frequency distribution, follow the steps outlined here. A table is provided to show the scores (x) and their corresponding frequencies (f):
| Score, x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|-----------------|---|---|---|---|---|---|---|---|
| Frequency, f | 4 | 1 | 3 | 2 | 2 | 3 | 5 | 2 |
### Explanation
1. **Total Frequency (N):** Add the frequencies to get the total number of observations.
\[
N = 4 + 1 + 3 + 2 + 2 + 3 + 5 + 2 = 22
\]
2. **Cumulative Frequency:** Calculate cumulative frequencies to determine where the median lies.
- For score 1: \( 4 \)
- For score 2: \( 4 + 1 = 5 \)
- For score 3: \( 5 + 3 = 8 \)
- For score 4: \( 8 + 2 = 10 \)
- For score 5: \( 10 + 2 = 12 \)
- For score 6: \( 12 + 3 = 15 \)
- For score 7: \( 15 + 5 = 20 \)
- For score 8: \( 20 + 2 = 22 \)
3. **Finding the Median:**
- The position of the median is \( \frac{N + 1}{2} = \frac{22 + 1}{2} = 11.5 \)
- The median lies between the 11th and 12th data points.
- Based on cumulative frequencies, both the 11th and 12th data points fall into the score of 5.
Thus, the median is **5**.
Please input the median using an integer or a decimal where indicated.](https://content.bartleby.com/qna-images/question/3881c1a6-f287-42d9-8e45-c704abc4145f/7e7af895-9320-4327-b9c7-558efa0b806d/162424t_processed.jpeg)
Transcribed Image Text:**Understanding Median in Frequency Distribution**
To find the median of given data within a frequency distribution, follow the steps outlined here. A table is provided to show the scores (x) and their corresponding frequencies (f):
| Score, x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|-----------------|---|---|---|---|---|---|---|---|
| Frequency, f | 4 | 1 | 3 | 2 | 2 | 3 | 5 | 2 |
### Explanation
1. **Total Frequency (N):** Add the frequencies to get the total number of observations.
\[
N = 4 + 1 + 3 + 2 + 2 + 3 + 5 + 2 = 22
\]
2. **Cumulative Frequency:** Calculate cumulative frequencies to determine where the median lies.
- For score 1: \( 4 \)
- For score 2: \( 4 + 1 = 5 \)
- For score 3: \( 5 + 3 = 8 \)
- For score 4: \( 8 + 2 = 10 \)
- For score 5: \( 10 + 2 = 12 \)
- For score 6: \( 12 + 3 = 15 \)
- For score 7: \( 15 + 5 = 20 \)
- For score 8: \( 20 + 2 = 22 \)
3. **Finding the Median:**
- The position of the median is \( \frac{N + 1}{2} = \frac{22 + 1}{2} = 11.5 \)
- The median lies between the 11th and 12th data points.
- Based on cumulative frequencies, both the 11th and 12th data points fall into the score of 5.
Thus, the median is **5**.
Please input the median using an integer or a decimal where indicated.
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