Chapter 10, Problem AP3.17CPT

To determine

To find out the correct option for which of the following statements is false.

Answer to Problem AP3.17CPT

Option (b) is the correct option.

Explanation of Solution

Now, we will check each of the statements given that whether it is true or false.

The first statement is true because a distribution of quantitative data is summarized by a measure of center and a measure of variation and the shape of the distribution. Thus, the measure of center does not summarize the distribution alone.

For the second statement, it is false because the mean and the standard deviation will change the same as the original measurements, because if the original measurements are converted to centimeters then the mean and the standard deviation are also converted to centimeters.

For the third statement, it is true because the histogram represent the data values by bars while there is a range of possible values for each data value at a bar and thus we cannot determine the exact data value from the bar.

For the fourth statement, it is true because if we add a data value that is equal to a mean in quantitative data then the variation from the mean in the data set decreases and the standard deviation measures the variations in the deviations from the mean which implies that the standard deviation decreases.

And from the fifth statement, it is also true because if a distribution is strongly skewed then the mean and the standard deviation will be strongly influenced by this skewnessand thus it is best not to use the mean and the standard deviation. Since the median and the interquartile range are not as strongly influenced by the skewness and it would then be better to use the median and the interquartile range.

Thus, from above we conclude that the statement is (b) is false. So, option (b) is the correct option.