Edexcel International A Level
Statistics 1 (YMA01)
Statistical Measures
Professional Revision Notes for Advanced Statistics
A comprehensive study guide covering central tendency, dispersion, frequency analysis, and statistical modelling
What You Need to Know
Measures of central tendency describe where the centre of data lies. The mean, median, and mode are the three main averages used in statistics, each with distinct advantages depending on the dataset.
Mean, Median, and Mode
Mean (x̄): The sum of all values divided by the number of values.
Formula: x̄ = Σx/n
Median: The middle value when data is arranged in order. If even number of values, the median is the average of the two middle values.
Mode: The value that occurs most frequently in a dataset. For grouped data, this is called the modal class.
✓ Key Fact: All three averages describe central tendency differently — mean uses all data, median ignores extremes, mode shows the most common value.
Choosing the Best Average
| Average |
Advantages |
Disadvantages |
Best Use |
| Mean |
Uses all data; precise calculations |
Affected by extreme values (outliers) |
Normal, symmetric distributions |
| Median |
Not affected by extremes; robust |
Ignores some data information |
Data with outliers (income, prices) |
| Mode |
Useful for categorical data |
May not exist or may be multiple modes |
Qualitative data; most popular item |
Finding Mean, Median, and Mode
Data: 14, 19, 19, 23, 27, 28
Mode: 19 (appears twice, all others once)
Median: (19 + 23)/2 = 21 (average of two middle values)
Mean: (14 + 19 + 19 + 23 + 27 + 28)/6 = 130/6 = 21.7 (3 s.f.)
Summary Statistics Notation
✓ Important Symbols:
- Σx: "Sigma x" — sum of all x values
- x̄: "x bar" — the mean of x values
- n: The number of data values
- Σxf: Sum of (value × frequency)
What You Need to Know
While central tendency tells us where data centres, measures of spread tell us how spread out the data is. Quartiles divide data into four equal parts, while range and interquartile range measure dispersion.
Quartiles and Percentiles
Lower Quartile (Q₁): The value at the 25th percentile — separates the lowest 25% from the highest 75%.
Median (Q₂): The value at the 50th percentile — the middle value.
Upper Quartile (Q₃): The value at the 75th percentile — separates the lowest 75% from the highest 25%.
Calculating Quartiles
For a dataset of size n:
- Lower Quartile:
- Upper Quartile:
Measures of Spread
Range: