Question

In the data set, what is the variance 68194

Answer 1

The answer is Your question is ambiguous,. Some answerers think you are asking about a dataset with a single value in it, and rightly say that the variance is zero.

But maybe you are asking what it means for the variance in a set of data to be 68194. If so, it means this: Let {x(i) | i = 1 .. n} be set the of numbers in the dataset. Let u be the mean of all the x(i). Then the variance is the sum, over all i, of (x(i) - u)**2. In your case that sum is 68194.

If the variance is small compared to the square of the mean, then the data are considered tightly concentrated around the mean. If large compared to the square of the mean, then the date is considered spread out or dispersed around the mean.

Answer 2

Question :- What is the variance of the data set :-

86, 49, 63, 90, 82, 98, 36.

Solution :-

we know that,

• Mean = sum of all observations / Total number of observations

so,

→ Mean of given data = xi = (86 + 49 + 63 + 90 + 82 + 98 + 36) / 7 = 504 / 7 = 72 .

then,

x (x - xi) (x - xi)²

86 (-12) 144

49 (-23) 529

63 (-9) 81

90 18 324

82 10 100

98 26 676

36 36 1296

⅀(x - xi)² = 3150

therefore ,

→ variance of the set of data = ⅀(x - xi)² / (n - 1)

→ variance of the set of data = 3150 / (7 - 1)

→ variance of the set of data = 3150 / 6

→ variance of the set of data = 525 (Ans.)

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