Statistical Tools and Interpretation
Mean, Median and Mode
The mean uses every observation. The median is the middle value after arranging observations. The mode is the most frequently occurring value.
Worked Example
For 8, 12, 15, 5 and 10: Mean = (8+12+15+5+10)/5 = 10.
If an extremely large value is added, the mean can change substantially. The median is often less affected by an extreme observation.
Correlation
Correlation describes the direction and degree of association between variables. Positive correlation means they tend to move together; negative correlation means they tend to move in opposite directions. Association alone does not prove causation.
Index Numbers
An index number measures relative change with reference to a base period, commonly set equal to 100. If a price index rises from 100 to 125, the measured level is 25% higher than the base-period level.
MCQs
- Which measure is most directly affected by every observation?
Answer: Mean.
Explanation: The mean is calculated using the value of every observation, so unusually large or small values can influence it strongly. - Does positive correlation prove that one variable causes another?
Answer: No.
Explanation: Two variables may move together because of a third factor, coincidence or another underlying relationship. Causation requires additional evidence.
Practice
Calculate mean and median for 4, 7, 7, 9, 13, 20. Then explain which measure would better represent a typical value if 200 were added to the dataset.