Question

A national chain of department stores ranks its 1,250,000 salespeople by the monetary value of their sales. Mary's sales are at the 38th

percentile. Ryan's sales are at the 73rd percentile.
(a) Which of the following must be true about Mary's sales?
About 38% of the salespeople had sales lower in value than Mary.
The value of Mary's sales were about 38% of the chain's total.
The value of Mary's sales was in the top half of all of the salespeople.
Mary sold $3800 in merchandise.
(b) Which of the following must be true about Mary's and Ryan's sales?
O Both Mary and Ryan had sales higher in value than the median.
O Both Mary and Ryan had sales lower in value than the median.
O Ryan's sales were higher in value than Mary's sales.
Mary's sales were higher in value than Ryan's sales.
X
5

Answer 1

Mary's sales are at the 38th percentile, meaning about 38% of salespeople had lower-valued sales than hers, but this does not mean her sales were 38% of the chain's total or that she sold $3800. Comparatively, Ryan's sales were at the 73rd percentile, indicating his sales were of higher value than Mary's.

Step-by-step explanation:

The question involves understanding scale scores, which are used to indicate the position of an individual within a distribution. In the scenario given, Mary's sales are at the 38th percentile. This means that about 38% of the salespeople had sales lower in value than Mary's sales. It is not possible to ascertain that Mary sold $3800 in merchandise purely based on the percentile information, nor can we conclude that her sales were 38% of the chain's total. Percentiles split the distribution into hundredths, they do not represent percentages of the total sum of sales.

When comparing the percentiles for Mary and Ryan, since Mary's sales are at the 38th percentile and Ryan's sales are at the 73rd percentile, this indicates that Ryan's sales were higher in value than Mary's sales. Mary's sales cannot be higher as her percentile is lower than Ryan's.

Mary's sales being at the 38th percentile does not mean she is in the top half of all salespeople, as being in the top half would require being at the 50th percentile or higher.