Statistics & Regression

Key concepts

• Mean = Σx / n
• Standard deviation σ (from calculator)
• Five-number summary: min, Q1, median, Q3, max
• Regression line: ŷ = a + bx
• Correlation coefficient r ∈ [−1, 1]

How it works

Use your calculator's statistics mode for σ, regression and r. Always interpret r in words (strong/weak, positive/negative) and check the box-and-whisker plot for skewness. For grouped data, use the class midpoints to estimate the mean and the upper class boundaries to draw the ogive. For ungrouped data, sort the values first, then find the median and quartiles. When asked to comment, compare the mean with the median for skewness and use the standard deviation or IQR to describe spread.

Step by step

1. Organise the data

List values, build a frequency table if needed.

2. Use the calculator

Enter data once, then read mean, σ, regression.

3. Interpret

Always describe what r means in context.

Worked examples

Given r = −0.92, describe the correlation.

1. |r| is close to 1 → strong
2. r is negative → negative correlation

Answer: Strong negative correlation

Find the mean and standard deviation of 2; 4; 4; 4; 5; 5; 7; 9

1. Mean = 40 ÷ 8 = 5
2. Squared deviations: 9; 1; 1; 1; 0; 0; 4; 16, which sum to 32
3. σ = √(32 ÷ 8)

Answer: Mean = 5 and σ = 2

The regression line is ŷ = 15 + 2,5x. Predict y when x = 12.

1. Substitute x = 12: ŷ = 15 + 2,5(12)

Answer: ŷ = 45

Find the five-number summary of 4; 7; 8; 10; 12; 15; 18

1. Seven sorted values: minimum 4 and maximum 18
2. The median is the 4th value: 10
3. Q1 is the median of 4; 7; 8, so 7, and Q3 is the median of 12; 15; 18, so 15

Answer: 4; 7; 10; 15; 18

Use an ogive to estimate the median mark of 60 learners

1. The median is at a cumulative frequency of n/2 = 30
2. Find 30 on the cumulative frequency axis and read across to the curve
3. Read down to the marks axis

Answer: The mark where the curve reaches a cumulative frequency of 30

A data set has mean 50 and standard deviation 8. Which values lie within one standard deviation of the mean?

1. x̄ − σ = 50 − 8 = 42
2. x̄ + σ = 50 + 8 = 58

Answer: The values from 42 to 58

Common mistakes

• Confusing median with mean
• Misreading the ogive scale
• Forgetting to interpret r in words
• Reading the median of an ogive from the wrong axis.

Frequently asked questions

Do I need to memorise regression formulas?

No — use your calculator. But you must know how to interpret a and b.

What does it mean if the mean is greater than the median?

The data is usually skewed to the right (positively skewed): a few large values pull the mean up.

What is an outlier?

A value far from the rest of the data. A common test flags values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR.