Download 11/11 Measures of Spread Day 2

FST – Measures of Spread Day 2
10/11/16
Name: _______________
Deviation:
The sample variance, denoted by s2, is the sum of squared deviations from the mean divided by n – 1. That
is, s =
2
 (x -
x)
2
n- 1
The sample standard deviation is the positive square root of the sample variance and is denoted by s. That
is, s =
 (x -
x)
2
n- 1
2
Note: The symbol s is used for population standard deviation and s is used for the population variance.
In the formula for the population standard deviation and variance the denominator is n, rather than n - 1 .
Steps to calculating the Variance and Standard Deviation:
1. Calculate the mean of the data.
2. Find the deviation (difference) of each value from the mean.
3. Square each deviation and add the squares.
4. Divide the sum of squared deviations by n - 1 . This is the variance.
5. Take the square root of the variance. This is the standard deviation.
Example: Cars sold in seven consecutive weeks.
x1 = 20, x 2 = 16, x 3 = 16, x 4 = 12, x 5 = 18, x 6 = 25, x 7 = 19
1.
Calculate the mean:
n
Observation
Deviation (x - x )
Squared Deviation (x - x )
2
 (x
2
i
- x) =
i= 1
n
s2 =
Sum =
Heights from FST period _____ , females.
2
- x)
i
=
i= 1
n- 1
n
 (x
s=
Example 2:
 (x
2
i
- x)
i= 1
n- 1
=
a.
Calculate the mean height:
Observation
Deviation (x - x )
Squared Deviation (x - x )2
Sum =
b.
Standard Deviation, s
d.
Q1 and Q3
Heights from FST period _____ , males.
c.
Median
e.
IQR
a.
Calculate the mean height:
Observation
Deviation (x - x )
Squared Deviation (x - x )2
Sum =
b.
Standard Deviation, s
d.
Q1 and Q3
c.
Median
e.
IQR
Grades of Stew Dent:
Gades
50
85
45
60
10
85
50
85
55
n
Calculate the mean:
Observation
 (x
2
i
- x) =
i= 1
Deviation (x - x )
Squared Deviation (x - x )
2
n
s2 =
 (x
2
i
=
i= 1
n- 1
n
 (x
s=
- x)
2
- x)
i
i= 1
n- 1
=
Sum =