Understanding Mean, Median, and Mode with Examples

In statistics, the mean, median, and mode are central measures used to describe the distribution of a given set of numbers. Let's delve into each of these concepts and illustrate them using an example set of numbers: 2, 2, 3, 5, 5, 5, 6, 8, 9.

Mean: The Average Value

The mean is the average value of the given observations. It is calculated by summing all the numbers and dividing by the count of numbers.

Calculation:

[text{Mean} frac{2 2 3 5 5 5 6 8 9}{9} frac{44}{9} approx 4.89]

Median: The Middle Value

The median is the middle value when all the observed values are sorted in ascending order. If there is an even number of observations, the median is the average of the two middle numbers.

In the given set of numbers: 2, 2, 3, 5, 5, 5, 6, 8, 9, there are 9 numbers, which is an odd count. Therefore, the median is the 5th number in the sorted list.

Calculation:

Sorted list: 2, 2, 3, 5, 5, 5, 6, 8, 9 Median: 5

Mode: The Most Frequent Value

The mode is the value that appears most frequently in a set of numbers. A set of numbers can have more than one mode if several values have the same highest frequency.

In the given set: 2, 2, 3, 5, 5, 5, 6, 8, 9, the number 5 appears three times, which is more than any other number.

Calculation:

[text{Mode} 5]

Range: The Difference between Maximum and Minimum

The range is the difference between the maximum and minimum values in the set of numbers.

Calculation:

[text{Range} text{Maximum} - text{Minimum} 9 - 2 7]

Comparison of Mean, Median, and Mode

For the set of numbers: 2, 2, 3, 5, 5, 5, 6, 8, 9, the calculations yield:

Mean: 4.89 Median: 5 Mode: 5 Range: 7

It is important to note that the mean and the mode are different values, whereas the median and mode are the same in this case because the mode, which is the most frequent number, happens to be in the middle of the sorted list.

Conclusion

Understanding the mean, median, and mode is essential in statistics and can provide valuable insights into the distribution and characteristics of a dataset. In this example, the mean, median, and mode were all distinct values, with the median and mode being the same due to the frequency of the middle number.

Additional Resources

For further reading on these topics, you can explore additional resources such as:

">Mean, Median, and Mode - Statistics How To ">Statistics Basics: Mean, Median, and Mode ">Understanding the Mode in Statistics