Relation Between Mean Median and Mode

Relation Between Mean Median and Mode

The Mean, Median, and Mode: Understanding the Relationship Between Them

In statistics, measures of central tendency are used to describe the typical or central value of a dataset. The three most commonly used measures of central tendency are the mean, median, and mode. While each measure provides different information about a dataset, there is a relationship between them that can help us better understand the distribution of the data.

The Mean

The mean is the arithmetic average of a dataset and is calculated by adding up all of the values in the dataset and dividing by the number of values. The mean is sensitive to extreme values, also known as outliers, and can be influenced by them.

For example, let's say we have the following dataset of test scores:

60, 70, 75, 80, 90, 95, 100

To calculate the mean, we add up all of the scores and divide by the number of students:

(60 + 70 + 75 + 80 + 90 + 95 + 100) / 7 = 81.4

Therefore, the mean test score for this dataset is 81.4.

The Median

The median is the middle value of a dataset when it is arranged in order from least to greatest. If there is an even number of values, the median is the average of the two middle values. The median is not sensitive to extreme values and is a more robust measure of central tendency than the mean.

Using the same dataset of test scores as before, the median would be:

60, 70, 75, 80, 90, 95, 100

The middle value is 80, so the median test score for this dataset is 80.

The Mode

The mode is the value that appears most frequently in a dataset. A dataset can have one mode, multiple modes, or no mode at all. The mode is not sensitive to extreme values and is often used for categorical data.

For example, let's say we have the following dataset of favorite colors:

red, blue, green, red, blue, yellow, red, green

The mode for this dataset is red, as it appears three times, which is more than any other color.

Relationship Between Mean, Median, and Mode

The relationship between the mean, median, and mode can help us understand the distribution of the data. In a symmetrical distribution, the mean, median, and mode are all the same value. This means that the data is evenly distributed around the center.

In a skewed distribution, the mean, median, and mode are different values. If the mean is greater than the median, the distribution is positively skewed, which means that the data is clustered towards the lower end of the range with a few extreme high values. If the mean is less than the median, the distribution is negatively skewed, which means that the data is clustered towards the upper end of the range with a few extreme low values.

Conclusion

The mean, median, and mode are all measures of central tendency that provide different information about a dataset. The mean is sensitive to extreme values, the median is not sensitive to extreme values, and the mode is used for categorical data. The relationship between the mean, median, and mode can help us understand the distribution of the data, and a symmetrical distribution will have all three measures equal.