MATH 140 Lecture Notes - Lecture 4: Interquartile Range, Standard Deviation
2/4/16
- With extreme data, the mean will not be represented so in that case we use median
- variance: σ!= !!!!"#$ !
!!!
- Ungrouped data variance
X
X – mean
(x – mean)2
60
-2.14
4.5796
60
-2.14
4.5796
60
-2.14
4.5796
62
-0.14
0.0196
63
0.86
0.7396
65
2.86
8.1796
65
2.86
8.1796
Mean = 62.14
0
30.8572
- standard deviation = variance
σ!=
Σx−mean !
n−1=
30.8572
6=5.142866667
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 = 5.142866667 =2.27
- Data with frequency variance
X
F
Xf
X – mean
(x – mean)2
F(x – mean)2
60
3
180
-2.14
4.5796
13.7388
62
1
62
0.14
0.0196
0.0196
63
1
63
0.86
0.7396
0.7396
65
2
130
2.86
8.1796
16.3592
7
435
30.8572
435 ÷ 7 = 62.14
𝜎=
30.8572
6=2.27
- Grouped data variance
Groups
F
X
Fx
X – mean
(x – mean)2
F(x – mean)2
60-62
10
61
610
-5
25
250
63-65
15
64
960
-2
4
60
66-68
20
67
1340
1
1
20
69-71
15
70
1050
4
16
240
60
3960
570
3960 ÷ 60 = 66
𝜎=
570
59 =3.11
- 14, 10, 20, 20, 40, 20, 10, 10, 20, 50, 10
- 10, 10, 10, 10, 14, 20, 20, 20, 20, 40, 50
o Q1 = 10, Q2 = 20, Q3 = 20
