If all values in a data set are the same then the sample variance is equal to?
Variance is the square of the standard deviation.
Answer: The variance of the data set in which each and every value is similar will be equal to 0.
Go through the explanation to understand better.
Variance is the degree of spread or change in the given data points. The variance is calculated in relation to the mean of the data. More the spread of the data, more will be the variance in relation to the mean.
The formula for variance :
σ2 = ∑ (X - μ)2 / N ,
σ2 = sample variance
X = Each data value
μ = mean of the data set
N = total number of data set.
Special case: When all the data set points are the same
In this case, the mean of the data set i.e. μ is same as each data value i.e. X
Thus, X - μ = 0
Hence, variance becomes 0.
In order to calculate the variance of the given dataset, we can make use of the online variance calculator.
So, the variance of the data set in which each value is similar will be equal to 0.