Basics of Statistics

Three ways to summarize a dataset

Imagine 7 friends report how many slices of pizza they ate at a party: 1, 2, 2, 3, 3, 3, 8. That last 8 is unusual, but it changes the story. Statistics gives us quick summary tools called mean, median, and mode.

• Mean: the average value
• Median: the middle value when numbers are ordered
• Mode: the value that appears most often

These are all measures of center, but they do not always agree. Think of them as three camera angles on the same scene:

• the mean looks at every value
• the median looks at position
• the mode looks for repetition

In this lesson, you'll learn how to compute each one and when each gives the clearest picture.

Mean: balancing the numbers

The mean is what most people call the average. Add all values, then divide by how many values there are.

Formula: mean = (sum of all values) / (number of values)

For 4, 6, 6, 7, 9:

mean = (4 + 6 + 6 + 7 + 9) / 5 = 32 / 5 = 6.4

You can picture the mean as the balance point of the data, like where a seesaw would level out. Because it uses every number, the mean is sensitive to unusually large or small values.

Example: for 2, 3, 3, 4, 20, the mean is

(2 + 3 + 3 + 4 + 20) / 5 = 32 / 5 = 6.4

Even though most values are near 3 or 4, the 20 pulls the mean upward. That's useful sometimes, but misleading other times.

Median: the middle seat in line

The median is the middle value after the data is put in order. If there is an odd number of values, pick the center one. If there is an even number, average the two middle values.

For 2, 3, 3, 4, 20, the ordered list is already shown, and the middle value is 3, so the median is 3.

For 5, 7, 8, 10, there are two middle numbers: 7 and 8.

median = (7 + 8) / 2 = 7.5

The median is like finding the student standing in the middle of a line. It cares about position, not how far away the largest number is. That makes it especially useful for data like incomes or house prices, where a few huge values can distort the mean.

Mode: the crowd favorite

The mode is the value that appears most often. It answers a different question: not “What is the average?” but “What happens most?”

For 1, 2, 2, 3, 3, 3, 8, the mode is 3 because it occurs three times.

A dataset can have:

• one mode: 4, 4, 5, 6 → mode is 4
• two modes: 2, 2, 5, 5, 7 → modes are 2 and 5
• no mode: 1, 2, 3, 4 → no value repeats

The mode is especially useful for categories, not just numbers. If 12 students choose favorite fruit and apple is chosen most often, then apple is the mode. So while mean and median need ordered numbers, mode can summarize repeated choices too.