Question

Which of the following is false?

(a) A measure of the center alone does not completely describe the characteristics of a set of data. Some measure of spread is also needed.

(b) If the original measurements are expressed in inches, the standard deviation would be expressed in square inches.

(c) One of the disadvantages of a histogram is that it doesn't show each data value.

(d) Between the range and the interquartile range, the IQR is a better measure of spread if there are outliers.

(e) If a distribution is skewed, the median and interquartile range should be reported rather than the mean and standard deviation.

Short answer

(b) If the original measurements are expressed in inches, the standard deviation would be expressed in square inches.

Step-by-step solution

Given Information

Need to find which of the following is false.

Explanation

a) Is true, having a mean doesn't full describe the data. It's possible to have multiple data with different spreads that all have the same mean.

c) Is true, histograms only show the class boundaries and the frequency (or relative frequency) between those boundaries.

d) Is true since the minimum and maximum are heavily influenced by outliers. The range takes into account of both minimum and maximum. IQR on the other hand takes into account the 25th and 75 th percentile which are more robust to outliers.

e) Is true, the mean and standard deviation are also more influenced by outliers than the median and interquartiles ranges. This is why nonparametric tests (distribution free) considers these quantities than the means.

Final Answer

The answer is b) If the original measurements are expressed in inches, the standard deviation would be expressed in square inches. This answer is false since variance is a measure of squared inches and standard deviation is the square root of the variance.