Concept explainers
(a)
To find: The mean and standard deviation of given data set.
(a)

Answer to Problem 23E
The mean is 12 and the standard deviation is 2√2 .
Explanation of Solution
Given:
The given line plot represents the data is given below:
Concept used:
Mean is given as:
ˉX=n∑i=1Xin
Standard deviation is given by:
σX=(√n∑i=1(Xi−ˉX)2n)
Here n is the total number of terms.
Calculation:
{8,10,10,14,14,16} The given data in discrete form is given as,
The mean and standard deviation are calculated as below:
Mean of given data is calculated as:
ˉX=8+10+10+14+14+166=726=12
Standard deviation is calculated as:
σX=√(8−12)2+(10−12)2+(10−12)2+(12−12)2+(14−12)2+(16−12)26=√486=2√2
Therefore, mean is 12 and the standard deviation is 2√2 .
(b)
To find: The mean and standard deviation of given data set.
(b)

Answer to Problem 23E
The mean is 20 and the standard deviation is 2√2 .
Explanation of Solution
Given:
The given line plot represents the data is given below:
Concept used:
Mean is given as:
ˉX=n∑i=1Xin
Standard deviation is given by:
σX=(√n∑i=1(Xi−ˉX)2n)
Calculation:
The given data in discrete form is given as:
{16,18,18,22,22,24}
The mean and standard deviation are calculated as below:
Mean of given data is calculated as:
ˉX=16+18+18+22+22+246=1206=20
Standard deviation is calculated as:
σX=√(16−20)2+(18−20)2+(18−20)2+(22−20)2+(22−20)2+(24−20)26=√486=2√2
Therefore, mean is 20 and the standard deviation is 2√2 .
Chapter 13 Solutions
EBK PRECALCULUS W/LIMITS
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