Math Problem Statement

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. 65  58  40  35  60  55  52  46  73  66 What is the​ mean?

Solution

To calculate the mean, add all the numbers together and then divide by the total count of numbers.

Given dataTo calculate the mean, add all the numbers together and then divide by the total count of numbers.

Given
65,58,40,35,60,55,52,46,73,6665, 58, 40, 35, 60, 55, 52, 46, 73, 66

Step 1: Find the Sum of All Values

65+58+40+35+60+55+52+46+73+66=55065 + 58 + 40 + 35 + 60 + 55 + 52 + 46 + 73 + 66 = 550

Step 2: Count the Total Number of Values

There are 10 values.

Step 3: Calculate the Mean

Mean=Sum of valuesTotal number of values=55010=55\text{Mean} = \frac{\text{Sum of values}}{\text{Total number of values}} = \frac{550}{10} = 55

So, the mean is 55.

Would you like me to find the median and mode as well, or provide further details?


  1. What is the median of a dataset, and how is it found?
  2. How do you calculate the mode in a dataset with multiple values?
  3. What would happen to the mean if we added another value to this dataset?
  4. Can the mean be lower than the smallest number in a dataset?
  5. How does an outlier affect the mean of a dataset?

Tip: In a dataset with an even number of values, the median is the average of the two middle numbers.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency

Formulas

Mean formula: Mean = Sum of values / Number of values
Median calculation for an even set
Mode: The most frequently occurring value(s)

Theorems

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Suitable Grade Level

Grades 6-8