CK-12-Basic Probability and Statistics Concepts - A Full Course

http://www.ck12.org Chapter 6. Normal Distribution Curves

σ^2 =

9 + 4 + 0 + 1 + 1 + 9 + 1 + 4 + 1 + 16

10

=

46

10

= 4. 6

σ=

√

4. 6 ≈ 2. 1

Step 5 can be written using the formulaσ=

√

∑(x−μ)^2

n

.

The standard deviation of the data set is approximately 2.1.

Now that you have completed all the steps, here is the table that was used to record the results. The table was
separated as the steps were completed. Now that you know the process involved in calculating the standard deviation,
there is no need to work with individual columns−work with an entire table.

TABLE6.19:

x (x−μ) (x−μ)^2

2 − 3 9

7 2 4

5 0 0

6 1 1

4 − 1 1

2 − 3 9

6 1 1

3 − 2 4

6 1 1

9 4 16

Practice

1. The following data was collected. 71 73 77 69 80 67 78 77 70 82 Fill
   in the chart below and calculate the standard deviation. The data represents a small population.

TABLE6.20:

Data(x) Mean(μ) Data−Mean(x−

μ)

Square of Data −

Mean(x−μ)^2

∑

2. The following data was collected: 55 48 65 70 48 59 67 44 Fill in the chart
   below and calculate the standard deviation. The data represents a sample.