Statistics
Measures of central tendency and dispersion
Measures of Central Tendency
Mean: the average — add all values and divide by the number of values.
Median: the middle value when data is ordered from smallest to largest.
Mode: the most frequent value.
These measures tell us about the 'centre' of a data set.
Example
Calculating Mean, Median, Mode
Data: 3, 5, 7, 7, 9, 10, 12
Mean = (3 + 5 + 7 + 7 + 9 + 10 + 12) / 7 = 53 / 7 ≈ 7.57
Median = 7 (the 4th value in 7 ordered values)
Mode = 7 (appears most often)
Measures of Spread
Range = highest value − lowest value.
Quartiles split ordered data into four equal parts: Q1 (lower quartile), Q2 (median), Q3 (upper quartile).
Interquartile range (IQR) = Q3 − Q1, showing the spread of the middle 50% of data.
Example
Five-Number Summary
Data: 2, 4, 5, 7, 8, 9, 11, 13, 15
Minimum = 2
Q1 = 4.5
Median (Q2) = 8
Q3 = 12
Maximum = 15
This summary is used to draw a box-and-whisker plot.
Note
Remember
The mean is affected by outliers (extreme values); the median is not. Always order data before finding the median or quartiles. Use box-and-whisker plots to visualise the five-number summary.
Key Vocabulary
MeanThe average of all values in a data set
MedianThe middle value in an ordered data set
ModeThe value that appears most often
RangeThe difference between the highest and lowest values
QuartileValues that divide ordered data into four equal parts
OutlierA value that is much higher or lower than the rest
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