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Explanation & Answer
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Solution
1. Given dataset is x: 7, 82, 101, 89, 99, 104, 79, 95
We can arrange the given data in ascending order as follows
x: 7, 79, 82, 89, 95, 99, 101, 104
n
∑ xi
a. Sample mean: x
⏨=
i=1
=
n
7 + 79 + 82 + 89 + 95 + 99 + 101 + 104
656
=
= 82
8
8
Ans. Hence, sample mean is 82.
b. Sample Standard deviatio
n
∑ (x - xi)2
i=1
s=
n-1
2
xi
xi - x⏨
xi - x⏨
7
7 - 82 = -75
5625
79
79 - 82 = -3
9
82
82 - 82 = 0
0
89
89 - 82 = 7
49
95
95 - 82 = 13
169
99
99 - 82 = 17
289
101
101 - 82 = 19
361
104
104 - 82 = 22
484
8
∑
i=1
xi - x⏨ = 6986
n
Therefore, sample standard deviation, s =
∑ (x - xi)2
i=1
=
n-1
6986
=
8-1
6986
= 31.59
7
Hence, s = 31.59
Interpretation: Since s = 31.59, the data seems to be highly scattered around the mean.
c. Sample Variance using three different methods:
(i) From the table (shown above), sample variance s2 =
n
∑ (x - xi)2
i=1
n-1
=
(ii) Using the sample standard deviation.
In part b, we have calculated sample standard deviation s = 31.59
sample variance = s2 = 31.592 = 997.93 ≈ 998
(iii) Sample variance can be...