Grade 6 Mathematics
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.
Add all values, divide by count
Middle value when ordered. If even count, average the two middle values.
Value that appears most often. Can have no mode or multiple modes.
Difference between largest and smallest values
Data: Quiz scores: 85, 92, 78, 92, 88
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
Data: 12, 15, 18, 22 (4 values - even count)
Find the two middle values: 12, 15, 18, 22
Average them: (15 + 18) / 2 = 33 / 2 = 16.5
Median = 16.5 (When there are two middle numbers, always find their average!)
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!
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
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? ________________
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? _______________________