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The mean is a measure of central tendency, often known simply as the average. It helps us understand the typical value around which the rest of the data can be compared. Calculating the mean involves summing all the data points and dividing the total by the number of data points.
For example, if we have data values such as 100, 150, and 200, the mean is calculated as follows:
\[\text{Mean} = \frac{100 + 150 + 200}{3} = 150\]
The mean is especially useful because it accounts for every value in our data set. However, it can be distorted by extreme values, known as outliers, which can make it a less reliable measure in some situations. In this exercise, the mean of tax return preparation costs is approximately 148.81, giving us a rough idea about the average cost for the service.

The median offers a different perspective. It is the middle value in a data set that has been arranged in order from smallest to largest. For odd-numbered data sets, the median is the exact middle value.
The median is calculated by simply picking the middle number when all values are listed in order. If there is an even number of observations, the median is the average of the two middle numbers.
In contrast to the mean, the median is not affected by outliers, making it a robust measure of central tendency when extremes are present.
In our exercise, with 21 observations in the data, the median is the 11th number, which is 130. This median tells us that half the values are less than 130, and half are more.

Quartiles divide a data set into four equal parts, helping understand the spread and central tendency better.
The first quartile (Q1) represents the 25th percentile, separating the lowest 25% of data from the rest, and the third quartile (Q3) marks the 75th percentile, dividing the lowest 75% from the highest 25%.

Calculating quartiles involves splitting the ordered data set accordingly:

• First Quartile (Q1): Located at the one-fourth position in the data. For 21 data points, it's between the 5th and 6th values, which comes out as 115 using interpolation.
• Third Quartile (Q3): Found three-fourths up the list. In our data, this lies between the 16th and 17th values. Interpolating these positions gives a third quartile of 187.5.

Quartiles provide a deeper insight into data distribution, helping identify where the bulk of data values lie.

Percentiles indicate the relative standing of a value in a dataset. They show the percentage of observations below a specific value, allowing for more detailed understanding of distribution than quartiles offer.
The 90th percentile, specifically, shows us the value below which 90% of points fall. It can be particularly useful in comparing high performance or extreme values within a dataset.
To calculate the 90th percentile, find the position corresponding to 90% of the data. For our data with 21 points, this is the 19.8th position. By interpolating between the 19th and 20th values (235 and 255), we determine the 90th percentile to be 251.
Understanding percentiles helps in situations where you're assessing the relative position within large datasets, like test scores or income levels.