Math Problem Statement
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?
67 94 7 84 80 1 24 65 69 60 72
Question content area bottom
Part 1
a. Find the mean.
The mean is
(Type an integer or a decimal rounded to one decimal place as needed.) Part 2 b. Find the median. The median is
(Type an integer or a decimal rounded to one decimal place as needed.) Part 3 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) enter your response here. (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) B. There is no mode. Part 4 d. Find the midrange. The midrange is
(Type an integer or a decimal rounded to one decimal place as needed.) Part 5 e. What do the results tell us? A. 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. B. 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. C. The jersey numbers are nominal data and they do not measure or count anything, so the resulting statistics are meaningless. D. Since only 11 of the jersey numbers were in the sample, the statistics cannot give any meaningful results. The mean is(Type an integer or a decimal rounded to one decimal place as needed.)The median is(Type an integer or a decimal rounded to one decimal place as needed.))Select the correct choice below and, if necessary, fill in the answer box to complete your choice.The midrange is(Type an integer or a decimal rounded to one decimal place as needed.)What do the results tell us?
Solution
Let's analyze the results:
- Mean: The mean jersey number is approximately .
- Median: The median jersey number is .
- Mode: The mode (most frequent value) is , which appears only once, making it somewhat trivial.
- Midrange: The midrange (average of the minimum and maximum values) is .
Interpretation:
- Correct interpretation is Option C: The jersey numbers are nominal data, meaning they serve as identifiers rather than quantities or measurements. Therefore, the resulting statistics don't provide meaningful insight into the players themselves.
Would you like more details, or do you have any questions?
Here are five related questions to explore:
- What is the range of the data?
- How does the standard deviation of the jersey numbers compare with the mean?
- If you added another jersey number, how would it affect the mean and median?
- Why is the mode not useful for this dataset?
- What does the midrange tell us about the spread of the jersey numbers?
Tip: For nominal data, measures like the mean or median aren't useful because they don't represent meaningful quantities.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Mean
Median
Mode
Midrange
Formulas
Mean = (sum of all values) / (number of values)
Median = middle value when data is ordered
Mode = most frequent value
Midrange = (min value + max value) / 2
Theorems
No major theorems directly apply, but the concepts are part of elementary statistics.
Suitable Grade Level
Grades 9-12
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