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.
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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