Understanding Averages: Mean, Median, and Mode

Averages are a way to summarize and describe the typical value of a set of data. There are three types of averages: mean, median, and mode.

1. Mean : The mean is calculated by adding up all the values in a dataset and dividing by the number of values. It is the most commonly used type of average.
2. Median : The median is the middle value in a dataset when the values are arranged in order. If there are an even number of values, the median is the average of the two middle values.
3. Mode : The mode is the value that appears most frequently in a dataset. If there is no value that appears more than once, then there is no mode.

For example, let's say we have the following set of exam scores: 80, 75, 90, 85, 70, 85. To find the mean, we add up all the values and divide by the number of values:

(80 + 75 + 90 + 85 + 70 + 85) / 6 = 84

So, the mean of this dataset is 84. To find the median, we need to arrange the values in order:

70, 80, 85, 90

Since there are an even number of values, the median is the average of the two middle values:

(80 + 85) / 2 = 82.5

So, the median of this dataset is 82.5. To find the mode, we need to look for the value that appears most frequently in the dataset:

The value 85 appears twice, so the mode is 85.

In summary, the mean is the sum of all the values divided by the number of values, the median is the middle value in a dataset arranged in order, and the mode is the value that appears most frequently in a dataset.