Q 733. When summarizing continuous data it is important to report both measure of central tendency (such as mean or median) and measure of dispersion (such as standard deviation or interquartile range). Still organizations, teams and people often emphasize and only report the measure of central tendency and ignore the measure of dispersion. What are the reasons for ignoring the measure of dispersion? How can this adversely impact decision making? Provide examples to support your answer.

 

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Reason for ignoring Measure of dispersion

1. The first and foremost reason I could think of is because of our natural awareness of mean and median (taught as part of your elementary mathematics in school days) and coupled with the fact that it is easy to calculate both mean and median

2. Awareness on Standard deviation and Range is relatively low for people in general (even though they might have learnt in their high school education) and these terms are usually known for people who are associated with any statistical related work or who show passion in statistical concepts or so. An additional pointer for a statistically aware person is that Standard Deviation can be lesser sensitive to outliers when compared with mean, Range is highly sensitive to outliers. 

 

3. People are just focused on the representative value around which the data clusters and does not bother about the variability involved in that (lack of awareness is the key as they are not aware of how important that variability factor is).

 

 

Impact in decision making:

Ignoring the measure of dispersion can result in not understanding

 1). the variability or the actual spread of the data 

 2). the outliers that exist in the given dataset

Example 1:

Let us try to see these impact with an example. We are considering here about how the data looks for a cricket bowler for just a small sample of 20 test matches (pls refer to the attached excel sheet). We want to see how the bowler's performance is over this period of 20 test matches.. As you can see the bowler's performance is good in the beginning of his/her career and then in the middle period, it is not looking good .. But in the latest matches that the bowler has played, it shows the bowler has taken good no. of wickets..

 

So barring the first and last few matches, the bowler has not performed well as shown by the mean which says for every match, the bowler is taking 4 wickets. So with mean , it is sensitive to outliers. If you look to the median, it shows the value as 2 which means it is not taking those few first and last matches where the bowler has taken more wickets...   

 

Now if we look at the holistic view of the bowler's performance in all the matches played, there is a lot of inconsistency (variability) in the middle phase for the bowler that is not captured by mean but Standard deviation shows the value as 3.77.  Even as this does not seem to be a significant difference when compared with the value of 4 (for mean) in this case, this gets drastically changed when the bowler performs well in some of the middle phase matches [changing values, say in few rows (from any of the rows - 9 to 20) in column D&E in the excel sheet can see a drastic change in the difference between mean and Standard Deviation values]. 

As we see here, mean is much sensitive to outliers and does not portray the true picture. Standrd deviation is relatively lesser sensitive to outliers and shows the variability.

 

Example 2: If we are to find the month in which the peak & least sales of cars were sold for a car dealer (for a particular brand of car), using the Range can help us get the data easily. By ignoring this measure of dispersion(which is highly sensitive to outliers), we will loose the ability to get this data in an easy manner 

 

Example from the Audit Industry: Statutory Audit

 

Scenario:

An audit team is evaluating the accounts receivable (AR) of a company. They calculate the average collection period (mean) as 45 days based on client data and present this finding in their statutory audit report. However, they fail to report the dispersion (e.g., standard deviation or range) of the collection periods across different customers.

 

Adverse Impact

1. Risk of Misrepresentation

While the average collection period is 45 days, the dispersion reveals significant variability. For example:

• Standard Deviation: ±20 days

• Some customers pay within 10 days, while others delay up to 90 days.

Ignoring this variability creates a misleading picture of the company’s cash flow stability. Stakeholders might assume the collection process is efficient when, in reality, some accounts are at a high risk of default.

2. Inadequate Risk Assessment

Without analyzing dispersion, the audit team might overlook customers with overdue payments or recognize revenue prematurely for those unlikely to pay within acceptable timeframes. This could:

• Lead to inflated revenue recognition.

• Result in non-compliance with accounting standards (e.g., IFRS or AS).

3. Implications for Management and Stakeholders

• Management Decisions: Based on the average, the company might not implement stricter credit controls or follow up aggressively with delayed customers, increasing bad debt risk.

• Investor Decisions: Investors might wrongly assume smooth cash flows and undervalue liquidity risk.

Organizations, teams and people often emphasize and only report the measure of central tendency and ignore the measure of dispersion primarily due to two reasons

a)      Low Statistical literacy and b) Unethical behaviour

A person in the organisation with low or no Statistical literacy would not know that ‘Standard deviation’ all alone is meaningless without context, and it must be considered relative to the mean (For instance, a standard deviation of 100 could be large if the mean is 100 but small if the mean is 1 billion).

Similarly, such individuals may may not recognise that the simplest numerical measure of dispersion in a data set that he/she is dealing with is the range. Instead, a range would be looked at potential capability of the team or the process. For example: Assuming every employee can match the performance of the best 1 out of 1000 employees (e.g., Mr. ABC with 5% errors, minimum or Mr. XYZ with INR 1M sales, maximum).

Average is looked at the ‘favourite number’ as its easier to understand and communicate to a broader audience, compared to dispersion measures like standard deviation or interquartile range.

Unethical behaviour can be the second reason, where people wilfully choose an inappropriate summary measure (for example, reporting the mean for a very skewed set of data without any measures of dispersion) to distort the facts to support a particular position.

Here is an example of reporting the measure of central tendency and ignoring the measure of dispersion and how did it adversely impact decision making

In Banking, Tele sales executives are responsible for generating revenue overphone,they are given tele calling data base in spreadsheets, while data analytics team would have segmented the clients basis various criteria. However, client allocations are rarely random.

In most tele calling teams, the average is looked at as a metric and the highest among the tele calling executives are rewarded .

From the below table it looks like Agent B has the highest revenue average and also the total but the standard deviation is the highest fo B .Upon closer inspection, it becomes evident that Agent B is capitalizing on a loophole by focusing excessively on affluent clients, who tend to have higher credit card limits and larger loan eligibility amounts.

Had measures of dispersion like standard deviation been reported alongside the mean, these suspicions would have been triggered earlier & such unethical practises may not have continued to distort the facts to support a particular position which in this example is about the loophole of calling & engaging with Affluent clinets  disproportionately.

This highlights the importance of considering measures of dispersion like standard deviation alongside central tendency metrics. Failure to do so can lead to poor decision-making, unfair rewards, and overlooked systemic issues

Category	Agent A Revenue (INR)	Agent B Revenue (INR)
Avg	498.85	525.85
Stdev	6.682853157	36.64664126
Total	9977	10517
Count of General clients engaged	16	6
Count of Affluent clients engaged	4	14

 

Daily performance of A and B

Day	Agent A Revenue (INR)	Agent B Revenue (INR)	Agent A Client Type	Agent B Client Type
1	503	592	General	Affluent
2	499	527	Affluent	General
3	505	539	General	Affluent
4	511	482	General	Affluent
5	498	515	General	Affluent
6	498	540	General	Affluent
7	511	492	General	General
8	505	550	Affluent	Affluent
9	497	513	General	Affluent
10	504	525	General	General
11	497	513	General	Affluent
12	497	606	Affluent	General
13	502	535	Affluent	General
14	487	496	General	Affluent
15	488	567	General	Affluent
16	496	490	General	Affluent
17	493	544	General	Affluent
18	502	462	General	General
19	494	486	General	Affluent
20	490	543	General	Affluent

 

Edited December 29, 20241 yr by RD RD

Some team members or leaders in the organization do not report measures of dispersion for the following reasons:

 

• Reporting only the mean or median, presuming it is the best practice or easiest.
• Lack of knowledge about calculating the standard deviation and interquartile range (IQR).
• To exclusively portray positive outcomes of the central tendency to management or clients, rather than underlying negative trends such as variance, IQR, etc.

 

Reporting only the measure of central tendency which will have an impact on decision making are:

 

• Incorrect conclusion since the dispersion measures like variability and IQR are excluded
• Uncovered potential risks since the outliers are ignored
• Incorrect forecasts since the underlying trends and patterns are not reported

Example:

 

For Client X, a team of four experienced and three new data abstractors are working. Each of them abstracted 200 images per month. 10% of their work is sampled the team's Median score is reported as 85%. Based on these results, the client approved onboarding three more new data abstractors to scale up the resources for their outsourced work.

 

Since the measure of dispersion is not reported, it resulted in the incorrect decision of allocating a few more new data abstractors while the existing new data abstractors maintained low accuracy. However, on reviewing the measure of dispersion, it is noted the Inter Quartile Range (IQR) is 45%.

 

Client X	Sampled	Correct	Incorrect	Accuracy
Experienced Employee 1	20	20	0	100%
Experienced Employee 2	20	19	1	95%
Experienced Employee 3	20	18	2	90%
Experienced Employee 4	20	17	3	85%
New Employee 1	20	12	12	60%
New Employee 2	20	10	10	50%
New Employee 3	20	8	8	40%
Overall	140	104	36	74%

 

• Q1 – Lower Quartile Part in the above-given data (Median Score of New Employee 1, 2, 3) – 50%

• Q2 – Median of the above-given data (Score of Experienced Employee 4) – 85%

• Q3– Upper Quartile Part in the above-given data (Median Score of Experienced Employee 1, 2, 3) – 95%

 

IQR = Q3 – Q1 = 95% - 50% = 45%

Reasons for Ignoring the Measure of Dispersion

1. Calculating central tendency and representing it is easier than measures of deviation.

2. Due to treating measures of deviation as complex, stakeholders tend to focus more on simpler metrics like mean and median.

3. Knowledge about the importance of these metrics may not be present within an organization.

4. The interpretation of such metrics and their importance in understanding variability may not be known or acknowledged.

5. Basing the decisions on assumptions that the data is closer to the central value without using dispersion to validate the finding.

6. Organizations may also remove these calculations intentionally to show better results and profits.

Adverse Impact on Decision-Making

1. There could be misrepresentation of data where due to negating or leaving out dispersion organisations may show inflated profit or revenue.

2. VK Sir gave an example that illustrates how an unfair distribution may result if we simply display the mean salary without accounting for the range of wages.

3. In project management, resource and time allocation may not be successful if we merely consider the average time needed to accomplish activities without considering how they will be distributed.

4. Without standard deviation being taken into account, if we base our decisions solely on the mean or median of the data, we tend to miss out on doing a complete risk assessment of any new strategies or projects.

 

In the end we can say that ignoring measures of dispersion leads to oversimplification, missing out on variability, and an increase in incorrect or flawed decisions. Reporting both central tendency and dispersion gives us the full picture of what the data represents, which in the end leads to better decisions.

 

It was a treat to read such brilliant answers quoting examples from different walks of businesses. Hence, I would recommend to read all answers.

 

Best answer has been given by R Rajesh for answering both the parts of the questions and supporting it by a very interesting example. Well done!