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? 45 31 38 97 33 29 74 32 46 51 42 (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:

a. Mean

Step1: Sum all data points

Sum = \( 45 + 31 + 38 + 97 + 33 + 29 + 74 + 32 + 46 + 51 + 42 \)
Calculate the sum: \( 45+31 = 76 \); \( 76+38 = 114 \); \( 114+97 = 211 \); \( 211+33 = 244 \); \( 244+29 = 273 \); \( 273+74 = 347 \); \( 347+32 = 379 \); \( 379+46 = 425 \); \( 425+51 = 476 \); \( 476+42 = 518 \)

Step2: Divide by number of data points (n = 11)

Mean = \( \frac{518}{11} \approx 47.1 \)

b. Median

Step1: Order the data

Ordered data: \( 29, 31, 32, 33, 38, 42, 45, 46, 51, 74, 97 \)

Step2: Find the middle value (n = 11, so 6th term)

Median = \( 42 \)

c. Mode

Step1: Check frequency of each number

All numbers appear once, so there is no mode (or all are modes with frequency 1). But typically, if no number repeats, we say there is no mode.

d. Midrange

Answer:

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

Final Answers:

a. Mean: \( \approx 47.1 \)
b. Median: \( 42 \)
c. Mode: No mode (all unique)
d. Midrange: \( 63 \)
e. C