Measures of Central Tendency • Topic 3 of 3

Choosing the Best Measure and Data Interpretation

Choosing the Right Measure of Central Tendency:

ScenarioBest MeasureWhy?
Data with no extreme valuesMeanUses all data, good for further calculations
Data with outliersMedianNot influenced by extreme values
Data with repeated valuesModeShows most common value
Categorical data (colors, brands)ModeOnly measure that works for non-numeric data
Symmetrical distributionMean = MedianBoth work well
Skewed distributionMedianBetter represents "typical" value

Interpreting Data Distributions:

  • Symmetric distribution: Mean = Median = Mode
  • Positively skewed (right-skewed): Mean > Median > Mode (tail on right)
  • Negatively skewed (left-skewed): Mean < Median < Mode (tail on left)

Practical Applications:

FieldUse of Central Tendency
EducationAverage test scores (mean), middle student performance (median)
BusinessMost common purchase (mode), average sale (mean)
HealthcareAverage patient recovery time (mean), typical wait time (median)
SportsAverage points per game (mean), most frequent score (mode)
Choosing the Right Measure of Central TendencyMeasureBest WhenDrawbackExampleMeanData is symmetricAffected by outliersAvg test scoreMedianOutliers presentIgnores actual valuesMedian incomeModeCategorical dataMay not be uniqueMost popular sizeQuick Rule: Use MEAN for balanced data, MEDIAN when skewed,MODE for most common category or when data repeats
Solved Examples
1
Worked Example

A company has salaries: 25, 30, 32, 35, 38, 40, 45, 48, 50, 200 (in thousands). Which measure best represents the typical salary?

Solution
  • Mean = \((25+30+32+35+38+40+45+48+50+200) ÷ 10 = 543 ÷ 10 = 54.3\) thousand
  • Median = average of 5th and 6th values (38 and 40) = 39 thousand
  • Mode = none
  • The outlier (200) pulls the mean up. Median (39) better represents typical salary

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Answer: Median (39 thousand) **Example 2:** A shoe store records sales: size 6 (12 pairs), size 7 (18 pairs), size 8 (15 pairs), size 9 (5 pairs). Which measure should the store use for inventory planning? *Solution:* - Mean = not meaningful for sizes - Median = not the best for business decision - Mode = size 7 (sold most frequently) - Store should stock most size 7 shoes - **Answer:** Mode (size 7) **Example 3:** Test scores: 65, 70, 72, 75, 78, 80, 82, 85, 88, 90. Is the distribution symmetric? *Solution:* - Mean = $(65+70+72+75+78+80+82+85+88+90) ÷ 10 = 785 ÷ 10 = 78.5$ - Median = average of 5th and 6th (78 and 80) = 79 - Mean (78.5) ≈ Median (79) → approximately symmetric - **Answer:** Yes, approximately symmetric

Key Points

  • Mean = best for symmetric data with no outliers
  • Median = best for data with outliers or skewed distributions
  • Mode = only measure for categorical data; best for finding most common value
  • In symmetric distributions: Mean = Median = Mode
  • In right-skewed: Mean > Median
  • In left-skewed: Mean < Median
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.Which measure is most affected by an extreme value (outlier)?
Explanation: The mean.
Q2.Which measure is best when there are outliers?
Explanation: The median.
Q3.Which measure shows the most common value?
Explanation: The mode.
Q4.The median is ___ by extreme values.
Explanation: Not affected.
Practice more MCQs → 📝 Assignment · 35 marks