Question

1. Using the sample 3, 4, 6, 1, 10, 6

• Find the median, mean, mode, and range

• Find the standard deviation

2. Using the sample 8, 5, 1, 5, 2, 3

• Find the median, mean, mode, and range

• Find the standard deviation

Answer 1

Solution:

x	x2
3	9
4	16
6	36
1	1
10	100
6	36
∑x=30	∑x2=198

Mean ˉx=∑xn

=3+4+6+1+10+66

=306

=5


Median :
Observations in the ascending order are :
1,3,4,6,6,10

Here, n=6 is even.

M=Value of(n/2)thobservation+Value of(n/2 )+1)thobservation /2

=Value of(6/2)thobservation+Value of(6 /2)+1)thobservation/2

=Value of3rdobservation+Value of4thobservation/2

=4+62

=5


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√198-(30)265

=√198-1505

=√485

=√9.6

=3.0984

The Range = Maximum value - Minimum value

= 10 - 1

= 9

The Range = 9

Solution:

x	x2
8	64
5	25
1	1
5	25
2	4
3	9
---	---
∑x=24	∑x2=128

Mean ˉx=∑xn

=8+5+1+5+2+36

=246

=4


Median :
Observations in the ascending order are :
1,2,3,5,5,8

Here, n=6 is even.

M=Value of(n2)thobservation+Value of(n/2)+1)thobservation/2

=Value of(62)thobservation+Value of(6/2)+1)thobservation/2

=Value of3rdobservation+Value of4thobservation/2

=3+52

=4


Sample Standard deviation S=√∑x2-(∑x)2nn-1

=√128-(24)26/5

=√128-96/5

=√32/5

=√6.4

=2.5298

The Range = Maximum value - Minimum value

= 8- 1

= 7

The Range = 7