Statistics and Data Analysis
Grade 9 · Math · Study Guide
Understand measures of center and spread, interpret data displays, and identify trends and outliers.
Statistics is the science of collecting, organizing, and interpreting data. The three main measures of center are mean, median, and mode. The mean (average) is the sum of all values divided by the count. The median is the middle value when data is ordered. The mode is the value that appears most often. Each measure can give a different picture of the same data.
Measures of spread describe how tightly clustered or spread out data is. Range = maximum − minimum. The interquartile range (IQR) = Q3 − Q1 covers the middle 50% of data and is resistant to outliers. Standard deviation measures how far values typically stray from the mean.
Data displays include histograms (frequency distributions), box-and-whisker plots (showing median, quartiles, and extremes), and scatter plots (showing relationships between two variables). An outlier is a data point that falls far from the rest. When outliers are present, the median is a better measure of center than the mean because the mean gets pulled toward the outlier.
| Measure | How Calculated | Best Used When |
|---|---|---|
| Mean | Sum ÷ count | Data is symmetric, no extreme outliers |
| Median | Middle value when ordered | Data is skewed or has outliers |
| Mode | Most frequent value | Categorical data or finding most common response |
Key terms
- Mean
- The arithmetic average; sum of data ÷ number of values
- Median
- The middle value in an ordered data set
- Mode
- The value that appears most frequently in a data set
- Range
- Maximum minus minimum value; a simple measure of spread
- IQR (Interquartile Range)
- Q3 − Q1; the spread of the middle 50% of data
- Outlier
- A data value much higher or lower than the rest of the data
Flashcards
- Mean
- Sum of all values divided by the number of values
- Median
- Middle value of an ordered data set; splits data 50/50
- Mode
- Most frequently occurring value in a data set
- Range
- Max − Min; simplest spread measure
- Outlier
- Data point far from the main cluster; distorts the mean
- IQR
- Q3 − Q1; resistant measure of spread for middle 50% of data
Practice questions
Find the mean of: 4, 7, 8, 9, 12
- 7
- 8
- 9
- 10
Show answer
Answer: 8
Mean = (4 + 7 + 8 + 9 + 12) / 5 = 40 / 5 = 8.
The median is always affected by outliers.
Show answer
Answer: False
The median is the middle value and is resistant to outliers; the mean is the measure most affected.
The range of the data set {3, 7, 9, 12, 15} is ___.
Show answer
Answer: 12
Range = 15 − 3 = 12.
In the data set {2, 4, 4, 6, 8}, what is the mode?
- 4
- 6
- 2
- 5
Show answer
Answer: 4
4 appears twice, more than any other value.
Which measure of center is most affected by an outlier?
- Median
- Mode
- Mean
- IQR
Show answer
Answer: Mean
The mean sums all values, so an extreme value pulls it significantly; median and mode are resistant.
Fun facts
- The average American watches about 3 hours of TV per day — but the median is lower because a few people watch 8+ hours and pull the mean up.
- Florence Nightingale was a pioneering statistician who used data visualizations to convince the British government to improve hospital sanitation in the 1850s.
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