Finding Sample Variance

1
Finding Sample Variance Standard Deviation
Using The Shortcut Formula

• Given The times, in seconds, required for a
  sample of students to perform a required task
  were

6,
10,
13,
11,
12,
8

• Find a) The sample variance, s2

b) The sample standard deviation, s
2
The Formula - Knowing Its Parts

• The calculation of a sample statistic requires
  the use of a formula. In this case, use

• s2 is s-squared, the sample variance

• ?x2 is the sum of squared xs, the sum of all
  squared data

• ?x is the sum of x, the sum of all data

• n is the sample size, the number of data

(Do you have your sample data ready to use?)
3
Finding Summations ?x and ?x2

• The shortcut formula calculates the variance
  without the value of the mean. The first step is
  to find the two summations, ?x and ?x2

Sample 6, 10, 13, 11, 12, 8
6
8
10
13
11
12
60
(6)2
(10)2
(13)2
(11)2
(12)2
(8)2
36
634
100
169
121
144
64
4
Finding the Numerator

• First, find the numerator

Previously determined values ?x2634, ?x60, n6
60
634
6
34
5
Finding the Answer (a)

• Lastly, find the denominator and divide. You
  have the answer!

6.8
The sample variance is 6.8
Note Variance has NO unit of measure, its a
number only
6
Finding the Standard Deviation (b)

• The standard deviation is the square root of
  variance

• Therefore, the standard deviation is

2.60768
2.6
The standard deviation of the times is 2.6 seconds
Note The unit of measure for the standard
deviation is the unit of the data