Find the standard deviation (rounded to the nearest unit) for the data indicated. Test Score Frequency 90 80 70 8 60 6. 50 4 40 1 30 2 5

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Topic Video
Question
### Understanding Standard Deviation Calculation

In this exercise, we will find the standard deviation (rounded to the nearest unit) for the data indicated.

Data is given as follows:

| **Test Score** | **Frequency** |
|----------------|---------------|
| 90             | 2             |
| 80             | 5             |
| 70             | 8             |
| 60             | 6             |
| 50             | 4             |
| 40             | 1             |
| 30             | 2             |
| 0              | 5             |

---

### Explanation

1. **Test Score**: Represents the scores achieved in a test.
2. **Frequency**: Indicates how many students received a particular score.

### Steps to Calculate Standard Deviation:

1. **Calculate the Mean (Average)**
    - Multiply each test score by its frequency to get the total sum of scores.
    - Divide the total sum by the total number of observations (sum of all frequencies).

2. **Calculate the Variance**
    - Subtract the mean from each test score and square the result to get squared differences.
    - Multiply these squared differences by their respective frequencies.
    - Find the average of these weighted squared differences.

3. **Standard Deviation**
    - Take the square root of the variance.

By following these steps, you will be able to find the standard deviation for the given test scores.
Transcribed Image Text:### Understanding Standard Deviation Calculation In this exercise, we will find the standard deviation (rounded to the nearest unit) for the data indicated. Data is given as follows: | **Test Score** | **Frequency** | |----------------|---------------| | 90 | 2 | | 80 | 5 | | 70 | 8 | | 60 | 6 | | 50 | 4 | | 40 | 1 | | 30 | 2 | | 0 | 5 | --- ### Explanation 1. **Test Score**: Represents the scores achieved in a test. 2. **Frequency**: Indicates how many students received a particular score. ### Steps to Calculate Standard Deviation: 1. **Calculate the Mean (Average)** - Multiply each test score by its frequency to get the total sum of scores. - Divide the total sum by the total number of observations (sum of all frequencies). 2. **Calculate the Variance** - Subtract the mean from each test score and square the result to get squared differences. - Multiply these squared differences by their respective frequencies. - Find the average of these weighted squared differences. 3. **Standard Deviation** - Take the square root of the variance. By following these steps, you will be able to find the standard deviation for the given test scores.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 4 images

Blurred answer
Knowledge Booster
Centre, Spread, and Shape of a Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman