A sample of 100 resistors has an average resistance of 50 ? and a standard deviation of 5 ?. A second sample of 100 resistors has an average resistance of 100 ? and a standard deviation of 5 ?. If the two samples are combined, the standard deviation of all 200 resistances will be __________.
i. less than 5 ?
ii. greater than 5 ?
iii. equal to 5 ?
iv. can’t tell from the information given
ii. greater than 5 ?
The figure on the left is a sketch of separate histograms for each group. The histogram on the right is a sketch of a histogram for the two groups combined. There is more spread in the combined histogram than in either of the separate ones. Therefore the standard deviation of all 200 resistances is greater than 5?.
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