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?
52    85    11    49    44    14   48    78   69    71   15

Let's analyze the given data step by step and calculate the required values:

Given dataLet's analyze the given data step by step and calculate the required values:

Given   
52, 85, 11, 49, 44, 14, 48, 78, 69, 71, 15

### (a) **Mean**:
The mean is the average of the numbers. It's calculated by adding all the numbers together and dividing by the total count of numbers.

\[
\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}
\]

\[
\text{Sum of values} = 52 + 85 + 11 + 49 + 44 + 14 + 48 + 78 + 69 + 71 + 15 = 536
\]

There are 11 values, so:

\[
\text{Mean} = \frac{536}{11} = 48.73
\]

### (b) **Median**:
The median is the middle value when the data is ordered from least to greatest. If there's an odd number of values, the median is the middle one; if there's an even number, it's the average of the two middle values.

First, let's arrange the numbers in ascending order:

11, 14, 15, 44, 48, 49, 52, 69, 71, 78, 85

Since there are 11 values, the median is the 6th value:

\[
\text{Median} = 49
\]

### (c) **Mode**:
The mode is the number that appears most frequently. In this case, each number appears only once, so:

\[
\text{Mode} = \text{No mode}
\]

### (d) **Midrange**:
The midrange is the average of the maximum and minimum values.

\[
\text{Midrange} = \frac{\text{Max value} + \text{Min value}}{2}
\]

Max value = 85, Min value = 11

\[
\text{Midrange} = \frac{85 + 11}{2} = \frac{96}{2} = 48
\]

### (e) **What do the results tell us?**

Since the data consists of jersey numbers, which are not quantitative variables but rather identifiers, the statistical values like mean, median, mode, and midrange don't have meaningful interpretations in the context of team performance or any inherent numerical property. These calculations are simply a mathematical analysis of arbitrary numbers.

Would you like any clarifications or further details on any of these steps?

Here are 5 related questions for you:
1. How is the mode different from the mean and median in terms of data interpretation?
2. Why might the midrange be considered less informative than the mean or median?
3. Can the median be influenced by extreme values in a data set? Why or why not?
4. What does it mean if a data set has no mode?
5. How would the results change if you added more numbers to the data set?

**Tip:** The median is often more representative of a "typical" value in a data set with outliers than the mean, which can be skewed by extreme values.

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? 52, 85, 11, 49, 44, 14, 48, 78, 69, 71, 15.

Learn how to calculate the mean, median, mode, and midrange for a set of jersey numbers from a sports team roster. Explore descriptive statistics concepts with step-by-step solutions using data from 11 players. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation