Data Analysis and Descriptive Statistics
Once the data is in, how do you make sense of it? Learn the mean, median, mode and range, when to use each, and how to display data - the analysis skills every Paper 2 rewards.
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Making sense of the numbers 📊
A study might collect hundreds of results. **Descriptive statistics** are the tools that **summarise** that data so you can see what it shows at a glance. Two jobs matter most: finding a **typical value** (an average - the mean, median or mode) and seeing how **spread out** the data is (the range). Get those right, pick the correct one for your data, and display it in the right graph - that is what Paper 2 rewards.
Four measures to know 🗂️
Three are averages (measures of central tendency); one measures spread (dispersion). Learn them, then the next steps put them to work.
Match each measure to its meaning 🔗
- Mean
- Median
- Mode
- Range
- Add all values and divide by how many there are
- The middle value once the data is in order
- The value that appears most often
- The highest value minus the lowest value
Find the mode 🎯
Seven participants recalled this many words: 4, 6, 6, 7, 6, 9, 5. What is the mode?
- 6, because it appears more often than any other value
- 7, because it is in the middle
- 5, because it is the smallest common value
- 9, because it is the highest
Calculate the mean ➗
An interactive activity.
Which average, and when? 📉
They are not interchangeable - each has a best use:\n\n- **Mean**: uses every value, so it is powerful - but a single **outlier** (an extreme value) can drag it off and make it misleading. - **Median**: ignores how extreme the end values are, so it is the safer choice when the data is **skewed** or has outliers. - **Mode**: the only average that works for **categories** (like favourite colour) or for finding the most common result.
The outlier problem 🧮
A set of reaction times is mostly around 200 ms, but one participant scored 900 ms. Which average best represents the typical result?
- The median, because it is not distorted by the one extreme value
- The mean, because it uses every value
- The range, because it shows the highest and lowest
- No average can be used with an outlier
Two kinds of data ⚖️
Before you analyse, know what kind of data you have - it decides which tools you can use.
Match each display to its use 📈
- Bar chart
- Histogram
- Scatter diagram
- Frequency table
- Compares separate categories, with gaps between the bars
- Shows continuous data in intervals, with bars that touch
- Shows the relationship between two variables
- Records how many times each value or category occurs
Which is quantitative? ✅
Select the TWO examples that are QUANTITATIVE data (numbers you can count or measure).
- The number of words each participant recalled
- Each participant's reaction time in milliseconds
- A written description of how a participant felt
- An interview transcript about someone's experience
How to find the median 🪜
An interactive activity.
Choose the right tool 🧭
An interactive activity.
Your turn ✍️
An interactive activity.
The grade-9 habit 🌟
A weaker answer just calculates an average. A grade-9 answer **chooses** the right one and **says why**. Remember the trade-off: the **mean** uses every value but is thrown off by an **outlier**; the **median** rides out outliers and skew; the **mode** is your only option for **categories**. And match the display to the data - a **scatter diagram** for a relationship, a **histogram** for continuous data, a **bar chart** for separate categories. Justifying the choice is the mark-winner.