Answer :
Answer with explanation:
Ques 1)
We know that the range of a data set is the difference between the maximum and the minimum value.
We are given a data set as:
45 93 60 72 15 45 81
on arranging the data in the increasing order we get:
15 45 45 60 72 81 93
Minimum value=15
Maximum value=93
Range=Maximum value-Minimum value
Range=93-15
Range=78
Ques 2)
We are given data point as:
63 54 62 59 52
on arranging the data in the increasing order we have:
52 54 59 62 63
The mean of data is calculated as:
[tex]Mean=\dfrac{52+54+59+62+63}{5}\\\\\\Mean=\dfrac{290}{5}\\\\\\Mean=58[/tex]
Now we calculate variance
Let mean be denoted by x'
x-x' (x-x')²
52-58= -6 36
54-58= -4 16
59-58=1 1
62-58=4 16
63-58=5 25
∑ (x-x')²=94
Now, variance is:
Variance=∑ (x-x')²/5
=94/5
= 18.8
Hence, variance is: 18.8
Ques 3)
We are given Variance=88
As standard deviation is the square root of variance.
Hence,
standard deviation=√88
=9.38
Ques 4)
We arrange the data in the increasing order as:
4 4 5 5 5 6 9
Now mean of the data is:
[tex]Mean(x')=\dfrac{4+4+5+5+5+6+9}{7}\\\\\\Mean=\dfrac{38}{7}\\\\\\Mean(x')=5.43[/tex]
(x-x') (x-x')²
-1.43 2.04
-1.43 2.04
-0.43 0.18
-0.43 0.18
-0.43 0.18
0.57 0.32
3.57 12.74
∑ (x-x')²/7=17.68/7=2.52
Hence Variance=2.52
Now standard deviation is the square root of variance.
Hence standard deviation=√2.52=1.6
Ques 5)
The box and whisker plot is attached to the answer.
Minimum value=6
Maximum value=21
Median=14
First quartile=9
Upper quartile=17
