Mean, median, and mode are measures of central tendency, which help us understand the "average" or typical value in a set of data. These values describe the middle or most common points in a data set.

1. Mean

The mean is what people usually refer to as the "average." It is calculated by adding up all the numbers in a data set and then dividing by the number of values in that set.

Formula for Mean:
Mean = (Sum of all values) / (Number of values)

Example of Mean:

Suppose we have the following set of numbers: 3, 5, 7, 9, 11. To find the mean:

• First, add the numbers together: 3 + 5 + 7 + 9 + 11 = 35
• Then, divide by the number of values (5 in this case): 35 ÷ 5 = 7

So, the mean is 7.

2. Median

The median is the middle number in a data set when the numbers are arranged in ascending (or descending) order. If there is an odd number of values, the median is the number in the center. If there is an even number of values, the median is the average of the two middle numbers.

Example of Median:

Consider the following set of numbers: 3, 5, 7, 9, 11.

• First, arrange the numbers in order: 3, 5, 7, 9, 11
• The middle number is 7, so the median is 7.

If the set was 3, 5, 7, 9, 11, 13, then the two middle numbers would be 7 and 9. The median would be the average of 7 and 9, which is 8.

3. Mode

The mode is the number that appears most frequently in a data set. A data set can have:

• No mode, if all the numbers are different.
• One mode, if one number appears more than others.
• Multiple modes, if two or more numbers appear the same number of times and more frequently than the others.

Example of Mode:

Consider the set: 2, 4, 4, 6, 8.

• In this set, 4 appears twice, while the other numbers appear once.
• So, the mode is 4.

If the set was 1, 2, 3, 4, 5, then there is no mode because all numbers appear only once.

Summary:

- The mean is the average of the numbers.
- The median is the middle value in the ordered data set.
- The mode is the most frequent number in the data set.

These measures help us summarize and understand the data more easily. Depending on the situation, one measure may be more useful than the others.

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