Question

If I don’t have a calculator, how can I assess the normality of a data set?

Answer 1

Hint: For solving this question you should know about the normality of a data set and normality tests. The normality tests are used to determine if a data set is well-modelled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed. And these tests can be done with the help of calculators and without the help of calculators.

Complete step-by-step solution:
According to the question it is asked, if I don’t have a calculator, how can I assess the normality of a data set. As we know that the normal distribution is a common probability distribution. It has a shape often referred to as a ‘bell curve’. The normal distribution is always symmetrical about the mean. We can assess the normality without any calculator, by computing a normality test. Usually, we will choose one of the normality tests (chi-square, Jarque Bera, etc). All these tests can be used under specific conditions. And these tests are only possible with the help of a calculator.
However, there is a calculator that is easier to compute than the above tests, named as normal counts. It can be used as a quick and intuitive test for normality. In a normal distribution the 68-95-99.7 rule applies. This rule says that in a normal distribution:
1. 68% of the observations lie within one standard deviation of the mean.
2. 95% of the observations lie within two standard deviations of the mean.
3. 99.7% of the observations lie within three standard deviations of the mean.
In order to check the normality, we will count the total observations in our data set that lie within 1, 2 and 3 standard deviations from the mean of that. And then after that we will compare them to the expected percentage values in a normal distribution (68%-95%-99.7%). For this we will use the following steps:
Step 1: Calculate the mean.
Step 2: Calculate the standard deviation.
Step 3: Count the number of observations within 1, 2 and 3 standard deviations from the mean.
Step 4: Compare the observed and expected percentage values.
And thus we will assess the normality of a data set without a calculator.

Note: While solving this problem take the mean and standard deviation of a data set very carefully and when you count the number of observations within 1, 2 and 3 deviations from the mean, then compare this as a percentage value with the standard or expected percentage values.