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Question

The variance of data set I, of 14 readings is 6.76. Data set II, is formed by multiplying each of the readings of data set I by 9 and data set III is formed by adding 7 to all the readings of data set I. Find the average of the standard deviations of data sets II and III.

The correct answer is

13

Variance of data set I = 6.76, so its standard deviation = \(\sqrt{6.76} = 2.6\).

Multiplying every reading by 9 multiplies the standard deviation by 9: SD of set II = 9 × 2.6 = 23.4.

Adding 7 to every reading shifts the data but does not change the spread: SD of set III = 2.6.

Average of the two standard deviations = \(\frac{23.4 + 2.6}{2} = \frac{26}{2} = 13\).

Hence, the answer is 13.

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Similar Questions

  1. The weights of 5 ear-heads of sorghum are 100, 102, 118, 124, 126 grams. Find the standard deviation.

    (Round off your answer to two decimal places.)


Important Questions from Variance and Standard Deviation

  1. Consider a population that is finite, and sampling is with replacement. If the variance of the population is 2176.8 with a sample size of 16, then the variance of the sampling distribution of means is:

  2. If \(\rm \displaystyle \sum_{i = 1}^{10}x_i = 110\)  and  \(\rm \displaystyle \sum_{i = 1}^{10}x_i^2 = 1540\)   then what is the variance?

  3. The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p - q)2 = 10000, then what is the value of n?

  4. The fourth central moment of a mesokurtic distribution is 243. Its standard deviation is:

  5. The standard deviation of the first 10 natural numbers is 3.028. What will be the standard deviation of the first 20 natural numbers?

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