📊 Statistics

Mean, median, mode, range & reading charts

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Describing a Set of Data

When we collect numbers — like test scores or temperatures — statistics helps us describe them with a single value. The four most common measures are below. We'll use the data set 4, 8, 6, 8, 4, 9, 8 as an example.

Mean (average)

\(\text{mean} = \dfrac{\text{sum}}{\text{count}}\)

\((4+8+6+8+4+9+8) \div 7 = 47 \div 7 = 6.71\)

Median (middle)

Sort, then take the middle

Sorted: 4, 4, 6, 8, 8, 8, 9 → median = 8

Mode (most common)

The value that appears most

8 appears three times → mode = 8

Range (spread)

\(\text{range} = \text{max} - \text{min}\)

\(9 - 4 = 5\)

Finding the Median

1. Sort the numbers from smallest to largest.
2. If there is an odd count, the median is the middle number.
3. If there is an even count, average the two middle numbers.
Example: 3, 5, 7, 9 → median = \((5 + 7) \div 2 = 6\)

Types of Charts

📊 Bar Chart

Compares amounts across separate categories using bar heights.

📈 Line Graph

Shows how something changes over time — great for trends.

🥧 Pie Chart

Shows parts of a whole as slices. All slices add up to 100%.

Tips

  • Always sort the data before finding the median.
  • A data set can have no mode, one mode, or several modes.
  • The mean is affected by very large or very small values; the median is not.
  • Read the chart's axis labels and scale before answering questions.