Mean Median Mode and Range from Frequency Tables Cheat Sheet

Key Facts

• The total frequency is the total number of data values, so $N = f_1 + f_2 + f_3 + \cdots$.
• The mean from a frequency table is $\bar{x} = \frac{\sum xf}{\sum f}$, where $x$ is a data value and $f$ is its frequency.
• To find the median, use the ordered positions after counting frequencies, not just the middle row of the table.
• If $N$ is odd, the median is the value in position $\frac{N + 1}{2}$.
• If $N$ is even, the median is the average of the values in positions $\frac{N}{2}$ and $\frac{N}{2} + 1$.
• The mode is the data value with the greatest frequency.
• The range is $\text{range} = \text{maximum value} - \text{minimum value}$.
• Values with frequency $0$ are not part of the data set and should not affect the mean, median, mode, or range.

Vocabulary

Frequency

The number of times a data value appears in a data set.

Mean

The balance point or average of a data set, found by dividing the total of all values by the number of values.

Median

The middle value of an ordered data set, or the average of the two middle values when there is an even number of data values.

Mode

The data value or values that occur most often in a data set.

Range

The difference between the greatest data value and the least data value.

Weighted Sum

The sum found by multiplying each data value by its frequency and adding the products, written as $\sum xf$.