Statistical Measures

Grade 6 Mathematics

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The Big Idea

Statistics help us make sense of data! The measures of center (mean, median, mode) tell us about the "typical" value, while range tells us about the spread.

MEAN (Average)

Add all values, divide by count

Sum / Count

MEDIAN (Middle)

Middle value when ordered. If even count, average the two middle values.

Order first!

MODE (Most)

Value that appears most often. Can have no mode or multiple modes.

Most frequent

RANGE (Spread)

Difference between largest and smallest values

Max - Min

Example: Find All Four Measures

Data: Quiz scores: 85, 92, 78, 92, 88

1

First, ORDER the data: 78, 85, 88, 92, 92

MEAN: (78 + 85 + 88 + 92 + 92) / 5 = 435 / 5 = 87

MEDIAN: 78, 85, 88, 92, 92 (middle of 5 values) = 88

MODE: 92 (appears twice, most frequent)

RANGE: 92 - 78 = 14

Example: Even Number of Values (Median)

Data: 12, 15, 18, 22 (4 values - even count)

1

Find the two middle values: 12, 15, 18, 22

2

Average them: (15 + 18) / 2 = 33 / 2 = 16.5

Median = 16.5 (When there are two middle numbers, always find their average!)

What About Outliers?

An outlier is a value much higher or lower than the rest. Outliers affect the mean A LOT but barely change the median!

Example with outlier: 10, 12, 14, 15, 100

Mean = 151/5 = 30.2 (pulled up by 100!)

Median = 14 (not affected by extreme value)

When there's an outlier, median is usually a better measure of center!

TRAP ALERT: Ordering Matters!

WRONG: Finding median of 25, 18, 30, 22, 15 without ordering first. (Student says 30 is the median)

RIGHT: Order first: 15, 18, 22, 25, 30. Now find middle: Median = 22

Your Turn: Find the Measures

1. Data: 7, 10, 12, 10, 6

Ordered: _____, _____, _____, _____, _____

Mean =   Median =

Mode =   Range =

2. Data: 25, 30, 35, 40, 35, 45

Ordered: _____, _____, _____, _____, _____, _____

Mean =   Median =

Mode =   Range =

3. Data: 100, 85, 90, 95, 88, 20 (Note the outlier!)

Mean =   Median =

Which measure better represents the "typical" value? ________________

When to Use Each Measure?

4. A store wants to know the most popular shoe size sold. Which measure should they use?

Answer:   Why? _______________________

5. House prices in a neighborhood are: $150,000, $160,000, $155,000, $1,200,000, $165,000. Which measure best represents the typical house price?

Answer:   Why? _______________________

Remember These Key Points!