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Concept explainers
a.
To calculate : the mean and standard deviation of the given data.
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 18PPS
The mean height of the players is
The standard deviation of the given data is
Explanation of Solution
Given information :
Consider the information given in the question:
The heights (in inches) of fifteen players in a NBA team:
Formula used :
Step1: Find the mean,
Step2: Find the square of the difference between each value in the set of data and the mean. Then sum the squares, and divide by the number of values in the set of data. The result is the variance.
Step3: Take the square root of the variance to find the standard deviation.
Calculation :
As per problem,
The data set:
The number of values in the data set
Step1: To find the mean, add the heights (in inches) and then divide by the number of values in the data set.
Therefore, the mean height of fifteen NBA players is
Step2: To find the variance, square the difference between each value and the mean. Then add the squares, and divide by the number of values.
Step 3: the standard deviation is the square root of the variance
b.
To calculate: the mean and standard deviation of the data after trade of players and describe the change in calculations.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 18PPS
The mean height of the players is
The standard deviation of the given data is
Due to trade of players the mean height decreases and the standard deviation increases.
Explanation of Solution
Given:
The heights (in inches) of
A player of
The height of Earl Boykins is
Formula used :
Step1: Find the mean,
Step2: Find the square of the difference between each value in the set of data and the mean. Then sum the squares, and divide by the number of values in the set of data. The result is the variance.
Step3: Take the square root of the variance to find the standard deviation.
Calculation:
As per the given problem,
The height of the player who was traded
Replace the height of the traded player from the given data with the height of Earl Boykins.
The new set of data is:
The number of values in the data set
Step1: To find the mean, add the heights (in inches) and then divide by the number of values in the data set.
Therefore, the new mean height of fifteen NBA players is about
Step2: To find the new variance, square the difference between each value and the mean. Then add the squares, and divide by the number of values.
Step 3: the new standard deviation is the square root of the variance
The meanand standard deviation of the given data before the trade was
The mean and standard deviation of the given data after the trade is
Therefore, the mean height decreases due to trade of players,but the standard deviation increases.
c.
To convert:each data value into centimeters and find the mean.
To convert the calculated mean to inches.
To compare the calculated mean (in inches) to that mean calculated in part (a).
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 18PPS
The mean height of the players is
The mean height in inches is
Explanation of Solution
Given:
The heights (in inches) of
Formula used :
To find the mean,
Calculation:
As per the given problem,
The heights (in inches) of
To convert the height of each player into centimeter, use conversion relation:
Thereforethe height in centimeters:
To calculate the mean, add the heights (in centimeters) and then divide by the number of values in the data set.
Therefore, the mean height (in centimeters) of fifteen NBA players is about
To convert the mean (in centimeters) to inches, use conversion relation
Therefore,
The calculated mean in inches is same as the mean calculated in part (a).
Chapter 12 Solutions
Algebra 1
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