StatisticsUnit 26 min read

Measures of Central Tendency (Mean, Median, Mode)

Unit 2 of Statistics: introduces the three fundamental measures of central tendency—mean, median, and mode—explains their calculation, properties, and appropriate use cases, and provides worked examples relevant to tourism and business data.

Padhai · Based on the official syllabus and past papers
Updated 7 Oct 2026

Key points

Mean is the arithmetic average, best for symmetric, outlier‑free data.
Median is the middle value, robust against extreme values.
Mode is the most frequent value, useful for categorical or discrete data.
Each measure has distinct advantages, disadvantages, and application contexts.
Understanding when to use each measure is critical for accurate data interpretation and decision‑making.

Unit 2: Measures of Central Tendency

1. Definitions

Measure	Symbol	Formula (for a sample of size $n$ )	Interpretation
Mean	$\overset{x}{ˉ}$	$\overset{x}{ˉ} = \frac{1}{n} i = 1 \sum n x_{i}$	Average value of the data set.
Median	$M$	Middle value after sorting; if $n$ even, average of two middle values.	Value that splits the data into two equal halves.
Mode	$m$	Value(s) that occur most frequently.	Most common observation.

2. How They Work

2.1 Mean

The mean is obtained by summing all observations and dividing by the number of observations. It is sensitive to every value in the data set, including outliers.

Mean calculation: Sum of values (4+5+6+7) = 22; Mean = 22/4 = 5.5 (red bar shows data distribution)

2.2 Median

To find the median, arrange the data in ascending order. If the number of observations is odd, the median is the middle value. If even, it is the average of the two middle values.

Median of odd dataset (3, 4, 5, 6, 7): Middle value = 5 (green dot)

2.3 Mode

The mode is identified by counting the frequency of each distinct value and selecting the one with the highest count. A data set can have no mode, one mode (unimodal), or multiple modes (multimodal).

Mode: Most frequent value(s) = 5 (appears twice)

3. Worked Example – Tourism Arrival Data

A travel agency recorded the number of tourists arriving at a popular hill station over 10 days:

Day	Tourists
1	120
2	135
3	110
4	145
5	130
6	125
7	140
8	150
9	115
10	128

Mean
$\overset{x}{ˉ} = \frac{120 + 135 + 110 + 145 + 130 + 125 + 140 + 150 + 115 + 128}{10} = \frac{1248}{10} = 124.8$

Median – Arrange in ascending order: 110, 115, 120, 125, 128, 130, 135, 140, 145, 150.
Median = average of 128 and 130 = 129.

Mode – All values appear once; no mode.

Interpretation

The average daily arrival is 124.8 tourists.
Half the days had arrivals below 129, half above.
No single arrival number dominates the data.

4. Comparison Table

Feature	Mean	Median	Mode
Sensitivity to outliers	High	Low	Low
Requires numeric data	Yes	Yes	Yes (can be categorical)
Best for	Symmetric, continuous data	Skewed or ordinal data	Categorical or discrete data
Computation	Sum / n	Middle value	Frequency count
Interpretation	Average	Central tendency	Most common

5. Advantages & Disadvantages

Measure	Advantages	Disadvantages
Mean	Simple, uses all data, useful for further statistical analysis.	Influenced by extreme values, not suitable for skewed data.
Median	Robust to outliers, works with ordinal data.	Does not use all data, less efficient for symmetric data.
Mode	Indicates most frequent occurrence, useful for categorical data.	May not exist or may be multiple; not informative about spread.

6. Applications in Tourism & Business

Context	Measure	Why it is used
Hotel occupancy rates	Mean	Calculates average occupancy over a period.
Bus travel times	Median	Provides typical travel time unaffected by traffic jams.
Ticket price distribution	Mode	Identifies the most common price point for pricing strategy.
Customer satisfaction scores	Mean	Gives overall satisfaction level.
Daily revenue	Mean	Helps forecast future earnings.

7. Real‑World Examples

7.1 eSewa – Mean Transaction Amount

eSewa calculates the average transaction value each month to assess user spending behavior. The mean is used because transaction amounts are continuous and the platform wants to capture the overall spending trend.

7.2 Daraz – Median Product Price

Daraz displays the median price of a product category to help buyers understand typical cost, especially when a few high‑priced items skew the average.

7.3 Ncell – Mode of Data Plan Usage

Ncell analyzes the most frequently chosen data plan among its subscribers. The mode indicates the plan that should be promoted or expanded due to high demand.

7.4 Kathmandu Traffic Routes – Median Travel Time

City planners use the median travel time between key points to evaluate congestion. The median is preferred over the mean because occasional traffic jams create extreme values that would distort the average.

8. In the Real World

Product	Idea Used	How It Is Applied
eSewa	Mean	Calculates average transaction amount per month to gauge customer spending patterns.
Daraz	Median	Shows median product price in a category to help shoppers compare typical costs.
Ncell	Mode	Determines the most common data plan chosen by users to inform marketing focus.
Kathmandu Traffic	Median	Uses median travel time between city zones to assess typical congestion levels.

Worked Real‑World Example – Bank Loan Interest
A bank offers a loan of NPR 1,000,000 with an annual interest rate of 12%. The monthly interest is calculated using the mean interest rate across all loans. If the mean rate is 12%, the monthly interest is:

$Monthly Interest = \frac{12%}{12} \times 1, 000, 000 = 10, 000$

The bank uses this mean rate to standardize loan terms across its portfolio.

9. Exam Tip

Practice calculation of all three measures for various data sets, including grouped data.
Know the sensitivity of each measure to outliers and skewness.
Be able to justify which measure is appropriate for a given data type (continuous, ordinal, categorical).
Solve past exam questions that involve finding mean, median, mode, and interpreting them in context.

Based on the TU BTTM syllabus for Statistics (STT301), unit 2.

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