Lesson 5: Averages and Probability

New Concept

We'll explore three ways to find a "typical" value in a dataset: the mean (average), median (middle value), and mode (most frequent). You'll also learn to calculate basic probability to measure an event's likelihood.

What’s next

Next up, you'll master these concepts through a series of interactive examples and practice cards for calculating mean, median, mode, and probability.

Property

The mean of a set of $n$ numbers is the arithmetic average of the numbers.

Examples

• To find the mean of 8, 12, and 4, you first add them: $8 + 12 + 4 = 24$. Since there are 3 numbers, you divide by 3. The mean is $\frac{24}{3} = 8$.

• A student's first three test scores were 85, 88, and 94. To find the mean score, he would add them and divide by 3. The mean is $\frac{85+88+94}{3} = \frac{267}{3} = 89$.

Property

The median of a set of data values is the middle value.

• Half the data values are less than or equal to the median.
• Half the data values are greater than or equal to the median.

Examples

• For the data set {9, 11, 12, 13, 15, 18, 19}, the numbers are already in order. The middle value is 13, so the median is 13.

Property

The mode of a set of numbers is the number with the highest frequency.

The frequency is the number of times a number occurs. So the mode of a set of numbers is the number with the highest frequency.

Examples

• In the list of miles run {2, 3, 5, 8, 8, 8, 13}, the number 8 appears three times, more than any other number. The mode is 8 miles.

Property

The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible.

Examples

• A fruit bowl contains 3 bananas and 2 apples, for 5 total fruits. The probability of choosing a banana is $\frac{3}{5}$, or $0.6$, because there are 3 favorable outcomes (bananas) out of 5 total outcomes.

• When rolling a single six-sided die, the probability of getting a 4 is $\frac{1}{6}$, since there is only one face with a 4 out of six total faces.