Question

If the variance of the data 2, 4, 5, 6, 8, 17 is 23.33, then the variance of 4, 8, 10, 12, 16, 34 is:
(a) 23.23
(b) 25.33
(c) 46.66
(d) 93.32

Answer 1

Hint: Use the rule that if the set of data is k times the set of data and if its variable is given as k then the former would have \[{{k}^{2}}\] times of the variance.

Complete step-by-step answer:
In this question, we are given the variance of the data 2, 4, 5, 6, 8, 17 which is 23.33. So, from this, we have to find the variance of 4, 8, 10, 12, 16, 34. Now, before proceeding, let us first learn about variance too. In probability theory and statistics, the variance is the expectation of the squared deviation of a random variable from its mean. The variance is the square of the standard deviation, the second central moment of the distribution, and the covariance of the random variable with itself. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. A variance is an important tool in the sciences, where statistical analysis of data is common. Informally, it measures how far a set of numbers is spread out from their average value.
Now in the question, we were given that for the data 2, 4, 5, 6, 8, 17, the variance is 23.33. So, if the value of the data is multiplied by 2, we get, 4, 8, 10, 12, 16, 34 whose variance we are asked to find. So, the values we got by multiplying by 2, the variance we will also get by multiplying it by \[{{2}^{2}}\] or 4 to the variance of the data 2, 4, 5, 6, 8, 17. As there is a rule, if a set of values are k times more than a particular set of values, then the variance of the former will be \[{{k}^{2}}\] times that of the latter one.
Hence, the variance of 4, 8, 10, 12, 16, 34 is \[{{2}^{2}}\times 23.33\] or 93.32.
Hence, the correct option is (d).

Note: Also, one can find using the formula by finding the mean of the data values. Then, find the average of the squared difference from the mean. The process will be a bit lengthy and tedious.