Present the measures of central tendency with suitable example

Measures of central tendency are statistical tools used to summarize a set of data by identifying a single value that represents the center or typical value of a distribution. The three most commonly used measures of central tendency are the mean, median, and mode. Each of these measures offers a different perspective on the data and is selected based on the nature of the data and the research question being studied.

### Mean

The mean, also known as the arithmetic average, is the most commonly used measure of central tendency. It is calculated by adding up all the values in a data set and then dividing the sum by the total number of values. The mean provides a good summary measure for data that is symmetrically distributed and is not heavily influenced by extreme values (outliers).

Formula for mean:

\[
\text{Mean} = \frac{\sum X}{N}
\]

Where:
- \( \sum X \) is the sum of all data points.
- \( N \) is the number of data points.

Example:
Consider the following data on the number of hours worked by a group of social workers in a week:

10, 12, 14, 16, 18

To calculate the mean:

\[
\text{Sum} = 10 + 12 + 14 + 16 + 18 = 70
\]

Now, divide by the number of data points (5):

\[
\text{Mean} = \frac{70}{5} = 14
\]

Therefore, the mean number of hours worked per week is 14.

The mean is especially useful when the data points are fairly evenly distributed and there are no significant outliers that could skew the average. However, when the data includes extreme values, the mean can be influenced by these outliers, making it less representative of the center of the distribution.

### Median

The median is the middle value of a data set when __________ ____ ________ ____ ____ _______ _______ ______ ______ ____ ___ _________.
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