What does it mean to say that IQ scores are normally distributed?

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One example of a variable that has a Normal distribution is IQ. In the population, the mean IQ is 100 and it standard deviation, depending on the test, is 15 or 16. If a large enough random sample is selected, the IQ distribution of the sample will resemble the Normal curve.

Do IQ scores follow a normal distribution?

For IQ tests the chosen mean is 100 an the standard deviation is 15. So by definition 95\% of a population will have an IQ between 100 – 15 * 1.96 and 100 + 15 * 1.96. The IQ follows a normal distribution by construction. There is no natural unit by which you can measure intelligence.

What does it mean for data to be normally distributed?

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graph form, normal distribution will appear as a bell curve.

Are normal distributions discrete?

Unlike the normal distribution, which is continuous and accounts for any possible outcome along the number line, a discrete distribution is constructed from data that can only follow a finite or discrete set of outcomes.

Why would data not be normally distributed?

Collected data might not be normally distributed if it represents simply a subset of the total output a process produced. This can happen if data is collected and analyzed after sorting.

Why is it important to test the normality of a distribution?

The two well-known tests of normality, namely, the Kolmogorov–Smirnov test and the Shapiro–Wilk test are most widely used methods to test the normality of the data. Normality tests can be conducted in the statistical software “SPSS” (analyze → descriptive statistics → explore → plots → normality plots with tests).

What is intelligence quotient IQ )? How do psychologists classify people on the basis of their IQ scores?

IQ means Intelligence Quotient (IQ) which refers to mental age divided by chronological age, and multiplied by 100. \According to psychologists, IQ scores are distributed in the population in such a way that the scores of most people tend to fall in the middle range of the distribution.

What is the normal distribution of the IQ scale?

As Ron Maimon has said in the comments, the IQ scale is defined so that it gives a normal distribution with mean 100 and standard deviation 15. This is possible for any test score with a continuous distribution f. If the subject’s score in the test is s, their IQ will be given by:

Why are IQ test “discrete scores” said to have normal shape?

Why IQ test “discrete scores” are said to have “Normal shape”. IQ test scores don’t increment in decimals, but in whole numbers (e.g., 138, 140, 150 etc.). In other words, IQ tests only provide discrete scores [not continuous] (No body can get an IQ score of $115.568…$).

What does a standard deviation of 15 mean on IQ tests?

The standard deviation is a measure of spread, in this case of IQ scores. A standard devation of 15 means 68\% of the norm group has scored between 85 (100 – 15) and 115 (100 + 15). In other words, 68\% of the norm group has a score within one standard deviation of the average (100).

What is the relation between IQ score and other statistical measures?

Although the IQ score is widely known as a psychological statistic, its relation to other statistical measures is lesser known. The best way to explain these measures and their relations is using the normal distribution, also know as the Bell Curve. The IQ score chart below shows a visual representation and scale of a normal distribution.