# Slovin’s Formula – (Explained with Examples)

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Slovin’s Formula is a formula that is used to determine what sample size should be chosen to study a given population depending on the error tolerance level of the investigator.

For example, suppose that you want to know about the voting preferences of a given population. It is not feasible to ask each and every person about their voting preferences. In such a situation, it is reasonable to select a random sample from the entire population and interview only those people who are selected. But this introduces scope for error in the study. We also need to decide how many people should be included in our sample.

Clearly, a larger sample will minimize the error and a smaller sample greatly increases the error rate. Generally, a 5% error rate is considered acceptable. Given an acceptable error limit, we can use Slovin’s formula to decide the size of the randomly selected sample.

### Slovin’s Formula:

Let ‘N’ denote the size of the population and ‘e’ denote the maximum acceptable error limit. Then the sample size ‘n’ can be calculated using the formula,

n=\frac{N}{1 + Ne^2}

### Example 1:

Suppose that a company wants to conduct marketing supply research to know about consumer preferences. The company estimates that a total of N = 10000 people are regular loyal customers of the company. How many of these people should be interviewed to understand customer preferences? Take the margin of error to be 5%.

Solution: We want to choose a random sample of size ‘n’ from the entire population of customers. Applying Slovin’s formula we get that, n=\frac{N}{1 + Ne^2} = \frac{10000}{1+10000\times 0.05^2} = \frac{10000}{26} = 384.61

This means that a total of 385 people should be randomly selected and interviewed to conduct research on consumer preferences.

### Example 2:

Suppose that the population size in a study is N=5000 and the margin of error is 3%. How many units should be chosen in a randomly selected sample?

Solution: By Slovin’s formula we get that, n=\frac{N}{1 + Ne^2} = \frac{5000}{1+5000\times 0.02^2} = \frac{5000}{3} = 1666.67

This means that a total of 1667 units should be randomly selected.

#### Remarks:

1. Slovin’s formula cannot be used to determine the sample size if the population size is very small.
2. As a general rule, it was suggested by Gay (1978) that the sample size should be 20% of the given population for small population sizes (less than 500), and the sample size should be 10% of the given population for population sizes greater than 1000.

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