1. S1 Measures of Dispersion The mean, variance and standard deviation

2. S1 Measures of Dispersion
Objectives:
To be able to find the variance and standard deviation for discrete and continuous data using excel

3. The marks scored in a test by seven students are 3,4,6,2,8,8,5
The marks scored in a test by seven students are 3,4,6,2,8,8,5. Calculate the variance and standard deviation. x 3 4 6 2 8 5
Variance = Σx² – Σx ²
n n _ x² 9 16 36 4 64 25
σ ² = 218 – 36 ² = 4.69
σ = √4.69 = 2.17
Σx = 36
Σx² = 218

4. Variance and standard deviation of discrete data
Variance = Σx² – Σx ²
n n _
Use excel to quickly work out the variance and standard deviation of the questions below
3, 9, 12, 24, 10, 21, 27, 16
45, 56, 61, 34, 50, 50, 66, 51, 48, 49, 38
18, 22, 30, 27, 19, 25, 2, 156
Compare the answers you got in Q1 and 2 to the answer for Q3.
Explain the difference

5. The variance and standard deviation from a frequency table
Number of rods (x)
Freq of rods (f) 35 3 36 17 37 29 38 34 39 26 fx
fx²
105
612
1073
1292
1014
3675
22032
39701
49096
39546
Σf=109
Σfx=4096
Σfx²=154050
Variance = Σfx² – Σfx ²
Σf Σf
Variance = – ²
σ ²=
σ = 1.109

6. Use Excel to quickly work out the variance and standard deviation of the question below4 2 5 17 6 22 7 15 8
Variance = Σfx² – Σfx ²
Σf Σf
Change the frequency for x=4 or x=8.
What happens to the standard deviation?
What happens when you change the frequency when x=6?
Explain why

7. Variance and standard deviation from a grouped frequency distribution
Height of plant (cm)
Freq (f)
0 < h ≤ 5 4
5 < h ≤ 10 15
10 < h ≤ 15 5
15 < h ≤ 20 2
20 < h ≤ 25
25 < h ≤ 30 1
Total
σ ² = – 285 ² =
σ = √
σ = 11.35

8. Describe the skewness of each of the data sets
Use excel to work out the standard deviation for the following sets of data X F 8 13 9 21 10 37 11 35 12 4 X F 23
127 24 90 25 56 26 17 27 8
Height F
5-10 6
11-16 15
17-22 21
23-28 56
29-34 52
Height F
25-34 20
35-44 24
45-54 37
55-64 42
65-74 22
75-84 16
Comment on and compare the standard deviation for each of the data sets
Describe the skewness of each of the data sets