Formula for Margin of Error: How to Calculate in Easy Steps

Tally Solutions | Updated on: March 16, 2022

• What is the margin of error?
• Confidence interval vs. margin of error: what’s the difference?
• Formula for margin of error (very simple)
• The extended margin of error formula
• 2 easy steps to calculate margin of error
• Comparing both margin of error formulas
• The importance of margin of error

Market research is meant to give a company an insight into market trends and customer behavior and other factors that could influence their business. However, as with most things, there is always the chance of an error creeping in. It is essential for a company to be aware of the margin of error that is possible before they study the results. This will indicate just how reliable the research data is and will tell you how much you can count on the results to make significant changes in the business. So, if the result of market research shows a narrow margin between two options, the error margin must be considered before interpreting the result.

The margin for error is not a constant or random number but can be calculated precisely using a formula. There are several formulae that can be used for the calculation and you can use the one that best suits the type of survey.

What is the margin of error?

A survey is meant to reflect information related to the general population. However, every person in the target population is impossible to survey. So most surveys target a sample size that is meant to represent the entire population. The margin for error is the possible difference or error in the survey of the sample group when compared to the hypothetical survey of the entire population. A common man would refer to the margin of error as ‘give or take’. For example, they would say, “80% of the people prefer their coffee hot, give or take 5%”. This 5% is indicative of the margin of error.

In statistics, margin of error is defined as the degree of error that could be present in the survey of a random sampling of people. The larger the margin of error the less reliable the results are. The margin of error is a vital number included in survey results that indicate how much confidence there is in the data obtained from the survey. It also tells you how much the data is representative of the entire population. A margin of error that is low indicates that the results are more reliable. So the margin of error tells us by how much less or more the resultant survey data could vary from the full population despite having been taken from a random sample.

Example: A clothing store runs a survey that questions 100 random customers a day to ask if they considered parking facilities essential. On an average 80 of 100 customers said that they did. So, the manager of the store reports to the owner that 80% of the customers thought that parking for visitors to the store was essential. However, when he says it he adds, “give or take 3.” This implies that he is sure that 80 of 100 customers thought so but there may be a difference of three which translates to 77 to 83 percent. The results however, are convincing enough to retain reserved parking spaces for the customers of the store.

Confidence interval vs. margin of error: what’s the difference?

The confidence level is the indication of how sure the person stating the statistics is of the results. It does link to the margin of error. A lower margin of error would naturally inspire a greater confidence level in the person presenting or using the survey.

Example: In the example above, let us say 50 out of every 100 customers surveyed answered that they considered parking essential. The store manager would state with 100% confidence that exactly 50% of the customers indicated that they consider parking essential. But, if he says that between 40% to 60% prefer parking, it shows that there is a margin of error and that the confidence level is also lower than 100%.

Formula for margin of error (very simple)

There are multiple formulae for margin of error and they can be used depending on the survey type.

The simplest margin of error formula is

Margin of error= 1/ √sample size

We can apply this margin of error formula to the example above:

Suppose the store surveyed 2000 people in total over the course of the survey;

Margin of error= 1/ √2000

= 1/ 44.72

= .022

Expressed as a percentage, it is 2.2% margin of error for the survey.

The extended margin of error formula

There is a more detailed margin of error formula that can also be used to calculate the margin of error.

 It is

√ (Sample proportion (1- Sample proportion) / sample size) x  Z score

2 easy steps to calculate margin of error

The Z score is calculated based on the confidence level

The following reference table is used to determine the Z score:

Using our store example:

80% of the store customers considered parking essential as opposed to 20% who did not.

√ (.80 x .20) / 2000

√0.00008

= .0089

Now multiply the Z score by the total

1.96 x .0089

= .017

Expressed as a percentage, the survey of the store customers has a 1.7 percent margin of error.

Comparing both margin of error formulas

Though different formulae were used the results were close to 2%. This is why, though there are two different formulae, the simpler margin of error formula is preferred. It is more straightforward to calculate even by the layman. Business software would give you the option to choose between either of the formulae.

The importance of margin of error

Surveys are a popular tool to gain insight into the opinions, preferences and trends in a sample population. However, the surveyor and the people who use the results must know exactly how reliable or unreliable the survey results are. Otherwise, there may be unwise decisions made based on an unreliable survey. This is also important because surveys usually take a response from a smaller sample population rather than the entire relevant population or target market. If the margin of error is lower, the survey results are more reliable. If the margin of error is higher, the results must be taken with a pinch of salt.

The margin of error should be paid attention to when the poll delivers a result that has two options that are very close. For example, in the store poll, if 49% of the customers said that they considered parking essential and 51% said that they did not, the two results are very close. When the margin for error is very close, the results of 49% and 51% could easily swing either way. The poll should not be relied upon and should be treated as inconclusive.

Read More:

• What Are Open Market Operations (OMO)?
• What Are Profitability Ratios? Definition, Types and Importance