Question

find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. what do the results tell us? 46 83 25 61 37 53 62 41 97 23 72 a. find the mean. the mean is 54.5 (type an integer or a decimal rounded to one decimal place as needed.) b. find the median. the median is 53 (type an integer or a decimal rounded to one decimal place as needed.) c. find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mode(s) is(are) (type an integer or a decimal. do not round. use a comma to separate answers as needed.) b. there is no mode. d. find the midrange. the midrange is 60 (type an integer or a decimal rounded to one decimal place as needed.) e. what do the results tell us? a. the midrange gives the average (or typical) jersey number, while the mean and median give two different interpretations of the spread of possible jersey numbers b. since only 11 of the jersey numbers were in the sample, the statistics cannot give any meaningful results. c. the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistics are meaningless. d. the mean and median give two different interpretations of the average (or typical) jersey number, while the midrange shows the spread of possible jersey numbers.

Explanation:

Step1: Analyze the nature of jersey numbers

Jersey numbers are used for identification. They are nominal data. Nominal data just categorizes things and doesn't have a numerical value in the sense of measurement or count.

Step2: Evaluate each option

• Option A: Midrange, mean and median are measures of central tendency (not spread for midrange in a meaningful way for nominal data). And for nominal data like jersey numbers, these measures don't really give a typical value as they are not numerical in a quantitative sense.
• Option B: Sample size of 11 is not the issue. The problem is the nature of the data (nominal).
• Option C: Since jersey numbers are nominal data (used for naming/identifying players, not for measuring or counting something like height or goals), calculating mean, median, mode and midrange is meaningless.
• Option D: Mean, median and midrange are all measures of central tendency (midrange is \(\frac{\text{min}+\text{max}}{2}\)). For nominal data, they don't give valid interpretations about the data as the data isn't quantitative.

Answer:

C. The jersey numbers are nominal data and they do not measure or count anything, so the resulting statistics are meaningless.