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The mean is what most people commonly know as the average. It's a measure of central tendency, meaning it's used to determine a central or typical value within a set of numbers. Calculating the mean involves a straightforward process:

• Add all the numbers together, giving you the total sum.
• Count the total number of values in the set.
• Divide the total sum by the number of values to find the mean.

In the case of the family’s cell phone bills, we added up all the bills to get a total of $738. Dividing this by the seven bills gives us a mean of approximately $105.43.

This number can sometimes be misleading if there are outliers. An outlier is a number significantly higher or lower than the other numbers in the set. For example, here, the $196 bill is an outlier that raises the mean. Thus, one might incorrectly infer that a typical bill is over $105. However, most bills are notably less, as shown by the median.

The median offers another way to identify the middle of a number set. It slightly differs from the mean, especially when your data includes variances like outliers. To find the median, you follow these steps:

• First, arrange all the values from lowest to highest.
• If the number of values is odd, the median is the middle value.
• If even, it’s the average of the two middle values.

For the cell phone bills, after arranging them, the median is simply the middle value of the sorted list: 92. This measure tells us that at least half the bills are less than or equal to $92, providing a better sense of the typical spending than the mean.

In many cases, such as here, the median is more representative than the mean because it isn’t skewed by extreme values like the $196 bill.

Skewness is a concept used to describe the symmetry or asymmetry of data distributions. When data is skewed, the mean and median will diverge. The more skewed to the right or left the data is, the more pronounced these differences become.

• Right-skewed data means there's a longer tail on the right side of the distribution.
• Left-skewed data has a longer tail on the left.
• In a symmetric distribution, the mean and median will be similar.

In our example, the high bill of $196 is an outlier that causes right skewness. This is why the mean ($105.43) is higher than the median ($92). The skewness can misrepresent the data if we're only looking at the mean to understand typical values.

Being aware of skewness allows you to choose the right measure of central tendency – mean or median – to best represent the data. Generally, when data is skewed, the median provides a better assessment of the central location of the data.