SOLUTION: How do I find the variance and the standard deviation in this problem? I know the range is 11 and the mean is 16.2.. The ages (in years) of a random sample of shoppers at a gam

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Question 1036440: How do I find the variance and the standard deviation in this problem?
I know the range is 11 and the mean is 16.2..
The ages (in years) of a random sample of shoppers at a gaming store are shown. determine the range, mean, variance, and standard deviation of the sample data set.
12, 17, 23, 13, 14, 17, 20, 16, 15, 15
The variance is...
The standard deviation is...
Found 3 solutions by Boreal, Theo, Edwin McCravy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Add them up and divide by the number in the sample: 162/10=16.2
Take the difference of each value from the mean and square it. Add all the squares and divide by 9, one less than the number in the sample, because it is a sample and not a population. That is the variance:15.45
Take the square root of the variance. That is the standard deviation: 3.29
Take the difference between the highest and the lowest. That is the range: 11.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
you need to calculate the sum of squares.
from that you can get the variance.
from that you can get the standard deviation.

the sum of squares is the sum of the square of the difference between each data element and the mean.

the variance is the sum of squares divided by the number of elements in the data set.

the standard deviation is the square root of the variance.

these rules apply to the population statistics only.

sample statistics divide by 1 less than the number of elements.

the attached excel spreadsheet shows you the details of what i mean.

$$$


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Here's what to do with a list of data.  
Start with this column of x values, add
and divide by the number of numbers to
get the mean, x.

     x 
    12 
    17 
    23 
    13
    14
    17
    20
    16 
    15
    15
  -----
10)162.0 
x = 16.2

Then you make another column where you subtract x = 16.2 from
each number in the x-column.
That column is labeled x-x
There is no use to add it, because if you do 
you will just get 0

     x       x-x       
    12      -4.2      
    17       0.8       
    23       6.8      
    13      -3.2      
    14      -2.2       
    17       0.8       
    20       3.8      
    16      -0.2      
    15      -1.2       
    15      -1.2       
  -----    -----           
10)162.0     0.0       
x = 16.2

We square each number in that column and
put those squares in a new column.  We
add them and divide by 1 less than the
number of numbers.           

     x       x-x      (x-x)²
----------------------------- 
    12      -4.2      17.64
    17       0.8       0.64
    23       6.8      46.24
    13      -3.2      10.24
    14      -2.2       4.84
    17       0.8       0.64
    20       3.8      14.44
    16      -0.2       0.04
    15      -1.2       1.44
    15      -1.2       1.44
  -----    -----      -----
10)162.0     0.0     9)97.60
x = 16.2            s²=10.8444...

The sample variance is 10.8444...

The sample standard deviation is the square root of
the variance, s = 3.293090409...

Edwin
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