Statistics (Measures of Center & Variability) • Topic 1 of 4

Mean, Median, Mode, Range

Measures of Center describe the typical value in a dataset.

Measure	Definition	Example: {2,4,4,6,9}
Mean	Sum divided by count	(2+4+4+6+9)=25 / 5 = 5
Median	Middle value when data is sorted	Sorted: 2,4,4,6,9 — Middle = 4
Mode	Most frequently occurring value	4 appears twice — Mode = 4
Range	Maximum minus minimum	9 - 2 = 7

When dataset has even count: Median = average of the two middle values.

Outliers affect the mean significantly but not the median.

FINDING MEDIAN:

Odd dataset: {2, 4, 4, 6, 9}
  Sorted: 2  4  [4]  6  9
                 ^
              Median = 4 (3rd of 5)

Even dataset: {2, 4, 6, 8}
  Sorted: 2  [4  6]  8
               ^
         Median = (4+6)/2 = 5

MEAN as balance point:
  Data: {2, 4, 4, 6, 9}  Mean=5
  Deviations: -3, -1, -1, +1, +4
  Sum of deviations = 0 (always!)

Solved Examples

Worked Example

Find mean, median, mode, range: {7, 3, 8, 3, 9, 6}

SolutionSorted: 3,3,6,7,8,9. Mean=36/6=6. Median=(6+7)/2=6.5. Mode=3 (appears twice). Range=9-3=6.

Worked Example

Test scores: 85,90,78,92,88. A new score of 65 is added. What is the new mean?

SolutionOld sum=433. New sum=433+65=498. New mean=498/6=83.

Worked Example

Set {5,7,9,11,x} has a mean of 10. Find x.

Solution(5+7+9+11+x)/5 = 10 => 32+x = 50 => x = 18.

Key Points

Mean is sensitive to outliers (extreme values)
Median is resistant to outliers
Mode is the most frequent value; a dataset can have no mode or multiple modes
Range measures spread (not center)

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The mean equals:

Explanation: Sum over count.

Q2.The median is the:

Explanation: Middle value.

Q3.The mode is the value that occurs:

Explanation: Most frequent.

Q4.The range equals:

Explanation: Max minus min.

Practice more MCQs → 📝 Assignment · 35 marks