Preyom Choudhury 100783615
1.
[6 marks]
Suppose you are given the following set of 28 observation values:
45, 50, 55, 60, 65, 70, 75, 75, 80, 80, 80, 80, 85, 85, 85, 85, 85, 85, 90, 90, 90, 90, 90,
90, 90, 90, 95, 100
Calculate the
(a) mean,
(b) median,
(c) variance,
(d)
standard deviation,
(e)
Q1 (the first quartile or 25
th
percentile),
(f)
Q3 (the third quartile or the 75
th
percentile).
Sum of all values:2240
Number of Values: 28
a)
x
=
x
1
+
x
2
+
x
3
+
...
+
x
n
n
x
=
x
1
+
x
2
+
x
3
+
...
+
x
28
28
x
=
45
+
50
+
55
+
...
+
100
28
x
=
2240
28
x
=
80
The value of the mean (
x
) is 80
b)
85
+
85
2
=
85
The median is 85
c)
x
i
−
x
¿
¿
¿
2
¿
∑
i
=
1
n
¿
S
2
=
¿