Question

Which of the following statements is false?

a. A measure of center alone does not completely summarize a distribution of quantitative data.

b. If the original measurements are in inches, converting them to centimeters will not change the mean or standard deviation.

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

d. In a quantitative data set, adding a new data value equal to the mean will decrease the standard deviation.

e. If a distribution of quantitative data is strongly skewed, the median and interquartile range should be reported rather than the mean and standard deviation.

Short answer

The option that is false is:

a. If the measurements were taken in inches, converting them to centimetres has no effect on the mean or standard deviation.

Step-by-step solution

 Step 1: Given information 

We have to tell which of the given statements is false.

Explanation 

(a)True, because a quantitative data distribution is summarised by a measure of centre, a measure of variation, and the distribution's shape. As a result, the measure of centre alone does not adequately characterise the dispersion.

(b) False; the mean and standard deviation will change in the same way as the original measurements, because the mean and standard deviation are likewise transformed to centimetres when the original data are converted to centimetres.

(c) True, because the histogram shows data values as bars, and each data value at a bar has a range of possible values, therefore we can't discern the exact data value from the bar.

(d) True, because adding a data value equal to the mean in quantative data reduces the variance from the mean in the data collection, and the standard deviation reflects the variation in departures from the mean, hence the standard deviation lowers.

(e) True, because if a distribution is extremely skewed, the mean and standard deviation will be heavily influenced by the skewness, so it's preferable not to use them. Because the skewness has less of an impact on the median and interquartile range, it is preferable to use the median and interquartile range.