The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation population data set. 2, 9, 15, 4, 15, 6, 12, 8, 5,9 The range is 13. (Simplify your answer.) The population mean is 8.5. (Simplify your answer. Round to the nearest tenth as needed.) The population variance is (Simplify your answer. Round to the nearest tenth as needed.)
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation population data set. 2, 9, 15, 4, 15, 6, 12, 8, 5,9 The range is 13. (Simplify your answer.) The population mean is 8.5. (Simplify your answer. Round to the nearest tenth as needed.) The population variance is (Simplify your answer. Round to the nearest tenth as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Statistics for Football Team Wins
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.
**Data Set:**
\[ 2, 9, 15, 4, 15, 6, 12, 8, 5, 9 \]
#### Calculations
1. **Range:**
The range is calculated as the difference between the maximum and minimum values in the data set.
\[
\text{Range} = \text{max} - \text{min} = 15 - 2 = 13
\]
**The range is** \( \boxed{13} \).
2. **Population Mean:**
The mean is the average of the data set, calculated by summing all the values and dividing by the number of values.
\[
\text{Mean} = \frac{2 + 9 + 15 + 4 + 15 + 6 + 12 + 8 + 5 + 9}{10} = \frac{85}{10} = 8.5
\]
**The population mean is** \( \boxed{8.5} \) (simplify your answer. Round to the nearest tenth as needed).
3. **Population Variance:**
The variance measures the spread of the numbers in the data set. It is calculated by finding the average of the squared differences from the mean.
\[
\begin{align*}
\text{Variance} &= \frac{\sum_{i=1}^N (x_i - \mu)^2}{N} \\
&= \frac{(2-8.5)^2 + (9-8.5)^2 + (15-8.5)^2 + (4-8.5)^2 + (15-8.5)^2 + (6-8.5)^2 + (12-8.5)^2 + (8-8.5)^2 + (5-8.5)^2 + (9-8.5)^2}{10}
\end{align*}
\]
Calculating each squared difference:
\[
\begin{align*}
(2 - 8.5)^2 &= 42.25](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5ff9c3f-9717-4427-81ca-9eaa3fb6edc8%2F17848839-1c59-461f-bc9b-3d09464b7e32%2Fhigjtwjo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistics for Football Team Wins
The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.
**Data Set:**
\[ 2, 9, 15, 4, 15, 6, 12, 8, 5, 9 \]
#### Calculations
1. **Range:**
The range is calculated as the difference between the maximum and minimum values in the data set.
\[
\text{Range} = \text{max} - \text{min} = 15 - 2 = 13
\]
**The range is** \( \boxed{13} \).
2. **Population Mean:**
The mean is the average of the data set, calculated by summing all the values and dividing by the number of values.
\[
\text{Mean} = \frac{2 + 9 + 15 + 4 + 15 + 6 + 12 + 8 + 5 + 9}{10} = \frac{85}{10} = 8.5
\]
**The population mean is** \( \boxed{8.5} \) (simplify your answer. Round to the nearest tenth as needed).
3. **Population Variance:**
The variance measures the spread of the numbers in the data set. It is calculated by finding the average of the squared differences from the mean.
\[
\begin{align*}
\text{Variance} &= \frac{\sum_{i=1}^N (x_i - \mu)^2}{N} \\
&= \frac{(2-8.5)^2 + (9-8.5)^2 + (15-8.5)^2 + (4-8.5)^2 + (15-8.5)^2 + (6-8.5)^2 + (12-8.5)^2 + (8-8.5)^2 + (5-8.5)^2 + (9-8.5)^2}{10}
\end{align*}
\]
Calculating each squared difference:
\[
\begin{align*}
(2 - 8.5)^2 &= 42.25
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman