Standard Deviation

Standard deviation shows the variation from your data. Here is a math problem to give an example of how to find standard deviation based on collected data.

Seven students on an intramural team weigh 148 lb, 155 lb, 143 lb, 154 lb, 145 lb, 164 lb and 141 lb. What is the standard deviation of the weight of these students.

1) Find the mean.
 148+155+143+154+145+164+141       = 150
                       7
2) Subtract the mean from each of the weights.
148-150 = -2
155-150 = 5
143-150 = -7
154-150 = 4
145-150 = -5
164-150 = 14
141-150 = -9

3) Square each of the differences from step 2.
(-2)^2 = 4
(5)^2 = 25
(-7)^2=49
(4)^2 = 16
(-5)^2 = 25
(14)^2 = 196
(-9)^2 = 81

4) Add up all your answers from step 3.
4+25+49+16+25+196+81 = 396

5)Divide the sum from step 4 by the number of weights to get the variance.
396   =56.571
 7

6) Square the answer from step 5 to find the standard deviation.
56.571 = 7.5
 7

Your standard deviation is 7.5

Mean, Median, and Mode

The figure below contains the salaries of different employees at a job. What is the mean, median, and mode.

Number           Type                       Salary
    1                 owner                    $26,900 
    5              Sales Person             $18,900
    3                Secretary                $16,100
    1               Custodian                $11,000


Mean
First you multiply the number of people in the area of work by the salary that area of work makes. This gives you the total cost for each area of work.

1 * 26,900 = 26,900
5 * 18,900 = 94,500
3 * 16,100 = 48,300
1 * 11,000 = 11,000

Then you add up all the total cost. This finds the sum of all the employees makings.

26,900 + 94,500 + 48,300 +11,000 = 180,700

Finally you divide it by the total number of employees. To Find your mean.

180,700  = 18,070
    10

Median
First you have to place all your salaries from least to greatest.

11,000    16,100    16,100    16,100    18,900    18,900    18,900    18,900    18,900    26,900

Then you find the one in the middle and that is your median.

Mode
The mode is the salary that appears the most.
In this case it is 18,900