Learning Objectives

By the end of this lesson, learners should be able to:

  • Define mean, median, and mode.
  • Calculate measures of central tendency step by step.
  • Interpret central tendency in business contexts.
  • Select the most appropriate measure for different datasets.

Meaning Of Central Tendency

Measures of central tendency describe the typical or central value in a dataset. They provide a single number that represents the overall level of performance.

Why Managers Use Central Tendency

Managers use averages to:

  • Estimate average customer spending,
  • Compare regional sales,
  • Set performance targets,
  • Forecast staffing needs,
  • Evaluate supplier performance.

Arithmetic Mean

The mean is the sum of all values divided by the number of observations.

Formula

Mean = Sum of values ÷ Number of observations

Worked Example

Monthly sales (USD thousands):

50, 60, 70, 80, 90

Step 1: Add the values

50 + 60 + 70 + 80 + 90 = 350

Step 2: Count observations

5

Step 3: Divide

350 ÷ 5 = 70

Interpretation

Average monthly sales are USD 70,000.

Business Meaning

If sales continue at this average level, annual sales are approximately USD 840,000.

Advantages And Limitations Of The Mean

Advantages

  • Uses all observations,
  • Easy to calculate,
  • Suitable for further statistical analysis.

Limitations

  • Highly affected by extreme values.

Median

The median is the middle value when data is arranged in order.

Example

Sales: 40, 50, 60, 70, 500

The middle value is 60.

Why Median Matters

The extremely high sale of 500 does not distort the median.

Business Interpretation

Typical customer spending is about USD 60,000, even though one customer spent much more.

Median is often preferred for:

  • Income,
  • Property prices,
  • Customer spending,
  • Executive compensation.

Mode

The mode is the most frequently occurring value.

Example

Delivery times (days):

2, 2, 3, 4, 4, 4, 5

Mode = 4 days.

Business Use

The mode identifies the most common customer experience.

A courier company may conclude that most deliveries arrive within four days.

Comparing Mean, Median, And Mode

Measure

Best Use

Sensitive to Outliers?

Mean

Symmetrical data

Yes

Median

Skewed data

No

Mode

Most common category/value

No

Skewness And Central Tendency

Symmetrical Distribution

Mean ≈ Median ≈ Mode.

Positively Skewed Distribution

Mean > Median.

Example: executive salaries.

Negatively Skewed Distribution

Mean < Median.

Example: customer satisfaction scores where most customers are highly satisfied.

Weighted Mean

Used when observations have different importance.

Example

Product

Sales

Weight

A

100

0.5

B

80

0.3

C

60

0.2

Weighted mean = (100×0.5) + (80×0.3) + (60×0.2) = 50 + 24 + 12 = 86

Interpretation

The weighted average sales score is 86, giving more importance to Product A.

Geometric Mean

Useful for growth rates.

Example

A company grows by:

  • Year 1: +10%
  • Year 2: +20%
  • Year 3: +5%

The geometric mean provides the average annual growth rate and is widely used in finance and investment analysis.

International Business Case

A luxury retailer in Paris analyzes customer spending:

  • Mean purchase = EUR 420
  • Median purchase = EUR 180

Management concludes that a small number of very wealthy customers are inflating the average. Marketing campaigns are redesigned to target both premium customers and the broader customer base.

Common Mistakes

  • Using the mean for highly skewed data.
  • Ignoring outliers.
  • Comparing means from datasets with different currencies.
  • Reporting averages without sample size.

Practical Exercise

Calculate mean, median, and mode for monthly revenues from stores in London, Dubai, Singapore, Toronto, and Sydney, then explain which measure best represents typical performance.

Learning Materials / Reference Materials

  • Newbold, Carlson & Thorne. Statistics for Business and Economics.
  • OpenIntro Statistics.
  • Excel AVERAGE, MEDIAN, MODE, and SUMPRODUCT documentation.

Lesson Summary

Measures of central tendency summarize the typical value in a dataset. Selecting the correct measure is essential for accurate business interpretation and decision-making.

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