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examBoard: AQA
examType: GCSE
lessonTitle: Normal Distributions
Normal distributions are one of the most important concepts in psychology and statistics. They help us understand how data is spread out and what's considered "typical" or "unusual" in a population. When we collect data on things like IQ scores, reaction times, or personality traits, the results often form a normal distribution.
Key Definitions:
The normal distribution is often called a "bell curve" because of its shape. In a perfect normal distribution:
Normal distributions are important in psychology because:
When we look at a normal distribution curve, we can see that most of the data falls near the middle, with fewer and fewer values as we move away from the centre. This pattern is incredibly common in psychological data.
IQ scores are designed to follow a normal distribution with a mean of 100 and a standard deviation of 15. This means most people have IQs between 85 and 115, while very high (above 130) or very low (below 70) scores are much less common.
Standard deviation is a measure of how spread out the data is from the mean. A small standard deviation means most values are close to the mean, while a large standard deviation means the values are more spread out.
This rule (sometimes called the empirical rule) helps us understand how data is distributed in a normal distribution:
About 68% of values fall within 1 standard deviation of the mean
About 95% of values fall within 2 standard deviations of the mean
About 99.7% of values fall within 3 standard deviations of the mean
Let's use our IQ example again. If the mean IQ is 100 and the standard deviation is 15:
Z-scores tell us how many standard deviations a particular value is from the mean. They're useful because they convert any normal distribution to a standard normal distribution (with a mean of 0 and standard deviation of 1).
The formula for a z-score is: z = (x - μ) / σ
Where x is the raw score, μ is the mean and σ is the standard deviation.
Example: If someone has an IQ of 130, their z-score would be:
z = (130 - 100) / 15 = 2
This means their IQ is 2 standard deviations above the mean, putting them in the top 2.5% of the population.
Normal distributions are used in many areas of psychological research:
Psychologists use normal distributions to interpret scores on cognitive tests like IQ tests, memory assessments and attention measures. This helps them determine if someone's performance is typical, above average, or potentially indicating a cognitive issue.
In educational psychology, normal distributions help interpret test scores and determine appropriate interventions. If a student scores significantly below the mean, they might need additional support.
Clinical psychologists often use the normal distribution when interpreting assessment results. For example, on a depression scale, scores that are 2 or more standard deviations above the mean might indicate clinically significant depression requiring intervention. Understanding where a person's score falls on the normal distribution helps psychologists make informed treatment decisions.
Not all psychological data follows a normal distribution. Sometimes data can be:
When data isn't normally distributed, psychologists need to use different statistical approaches to analyse it properly.
Let's look at a practical example. A psychologist measures reaction times (in milliseconds) for 100 participants in a simple task:
Using the normal distribution, we can predict:
If someone has a reaction time of 190ms, their z-score would be:
z = (190 - 250) / 30 = -2
This means they're 2 standard deviations faster than the average person - quite speedy!
Understanding normal distributions helps psychologists:
Normal distributions are a fundamental concept in psychology that helps us make sense of human behaviour, cognition and emotion in a systematic way.
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