Math Problem Statement

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Part 1

The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the​ mean, median, and mode of the listed numbers.

5353  

6868  

7070  

6767  

7676  

3838  

3030  

6161  

4242  

3535  

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Part 1

What is the​ mean? Select the correct choice below​ and, if​ necessary, fill in the answer box within your choice.

A.

The mean is

enter your response here.

​(Round to one decimal place as​ needed.)

B.

There is no mean.

Solution

To find the mean of the listed numbers, follow these steps:

  1. List the numbers:

    • 53, 68, 70, 67, 76, 38, 30, 61, 42, 35
  2. Add all the numbers together: 53+68+70+67+76+38+30+61+42+35=54053 + 68 + 70 + 67 + 76 + 38 + 30 + 61 + 42 + 35 = 540

  3. Count the total number of values:

    • There are 10 numbers.
  4. Calculate the mean: Mean=Sum of the numbersNumber of values=54010=54.0\text{Mean} = \frac{\text{Sum of the numbers}}{\text{Number of values}} = \frac{540}{10} = 54.0

So, the mean is 54.0.

Answer:

A. The mean is 54.0 (rounded to one decimal place).

Would you like to explore the median and mode, or have any other questions?


Here are 5 questions to deepen your understanding:

  1. What is the formula for finding the median of a data set?
  2. How does the mode differ from the mean and median?
  3. Why might there be no mode in a data set?
  4. How does the size of a sample affect the mean?
  5. What are some situations where the median is more useful than the mean?

Tip: Always arrange numbers in order when calculating the median!

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Median
Mode

Formulas

Mean = (Sum of the numbers) / (Number of values)
Median: Middle value of an ordered data set
Mode: Most frequently occurring value in a data set

Theorems

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Suitable Grade Level

Grades 6-8