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

1111

players randomly selected from the roster of a championship sports team. What do the results tell​ us?

88    

7373    

66    

5959    

99    

2626    

1212    

6262    

3939    

1919    

44****    Question content area bottom

Part 1

a. Find the mean.

The mean is

enter your response here.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

Part 2

b. Find the median.

The median is

enter your response here.

​(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

enter your response here.

​(Type an integer or a decimal rounded to one decimal place as​ needed.)

Part 5

e. What do the results tell​ us?

A.

Since only

1111

of the jersey numbers were in the​ sample, the statistics cannot give any meaningful results.

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.

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.

Solution

numpy as np

Jersey numbers of the players

jersey_numbers = [88, 73, 66, 59, 99, 26, 12, 62, 39, 19, 44]

a. Calculate the mean

mean = np.mean(jersey_numbers)

b. Calculate the median

median = np.median(jersey_numbers)

c. Calculate the mode

(unique, counts) = np.unique(jersey_numbers, return_counts=True) max_count = np.max(counts) modes = unique[counts == max_count]

d. Calculate the midrange

midrange = (min(jersey_numbers) + max(jersey_numbers)) / 2

mean, median, modes.tolist(), midrangeHere are the results for the given data:

a. Mean: The mean is approximately 53.4 (rounded to one decimal place).

b. Median: The median is 59.0.

c. Mode: There is no mode since all values occur only once.

d. Midrange: The midrange is 55.5.

e. What do the results tell us? The correct interpretation is: C. The jersey numbers are nominal data and do not measure or count anything, so the resulting statistics are meaningless.

Would you like further clarification on these results?

Here are 5 related questions for exploration:

  1. How do the mean and median compare when the data set is highly skewed?
  2. Can the mode ever provide useful insights in nominal data like jersey numbers?
  3. How would the midrange change if there was an outlier in the data?
  4. What types of data are appropriate for calculating the mean, median, and mode?
  5. Can you provide a real-world scenario where these statistical measures are meaningful?

Tip: Always assess whether the type of data supports the statistical measures you want to calculate. Nominal data is typically analyzed using counts or proportions rather than means or medians.

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Math Problem Analysis

Mathematical Concepts

Statistics
Descriptive Statistics
Mean
Median
Mode
Midrange

Formulas

Mean: (Sum of all values) / (Number of values)
Median: Middle value when data is ordered
Mode: Value(s) that appear most frequently
Midrange: (Minimum value + Maximum value) / 2

Theorems

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Suitable Grade Level

Grades 8-10