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?

4949

6565

6767

8686

1010

3232

6969

2424

3838

4747**** 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.

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.)

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?

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.

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.

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

Since only

1111

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

Solution

import numpy as np from scipy import stats

Data

jersey_numbers = [49, 65, 67, 86, 10, 22, 32, 69, 24, 38, 47]

Calculations

mean_value = np.mean(jersey_numbers) median_value = np.median(jersey_numbers) mode_value = stats.mode(jersey_numbers, keepdims=True)[0][0] midrange_value = (min(jersey_numbers) + max(jersey_numbers)) / 2

mean_value, median_value, mode_value, midrange_value(46.27272727272727, 47.0, 10, 48.0)(46.27272727272727, 47.0, 10, 48.0)successHere are the computed statistics for the given jersey numbers:

a. The mean is approximately 46.3.

b. The median is 47.

c. The mode is 10.

d. The midrange is 48.0.

e. The results tell us:

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

Jersey numbers are categorical and serve as identifiers rather than measurements. As such, interpreting these statistics does not provide meaningful insights.

Would you like further clarification or additional analysis? Here are some related questions you could explore:

How is the mean affected by extreme values in data?
Why is the mode useful for nominal data?
What is the significance of midrange in numerical datasets?
How does the median compare to the mean in skewed data?
Can jersey numbers be used meaningfully in any statistical context?

Tip: Always verify whether your data type supports the statistical measures you want to calculate.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency
Nominal Data Analysis

Formulas

Mean = Sum of all values / Total number of values
Median = Middle value when data is arranged in ascending order
Mode = Most frequently occurring value
Midrange = (Minimum value + Maximum value) / 2

Theorems

Suitable Grade Level

Grades 8-10

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