Normally distributed
Definition
A normally distributed variable follows a bell-shaped curve, symmetrical around its mean. This distribution is defined by its mean and standard deviation.
5 Must Know Facts For Your Next Test
- The total area under the normal distribution curve is equal to 1.
- Approximately 68% of data falls within one standard deviation of the mean.
- 95% of data falls within two standard deviations of the mean.
- The normal distribution is important for hypothesis testing because many test statistics are assumed to be normally distributed under the null hypothesis.
- The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as the sample size grows.
Review Questions
- What percentage of data falls within two standard deviations from the mean in a normal distribution?
- Why is the normal distribution important in hypothesis testing?
- How does the Central Limit Theorem relate to normal distributions?
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Related terms
Mean: The average value of a set of numbers, calculated by dividing the sum of all values by their count.
Standard Deviation: A measure of dispersion that indicates how spread out values are around the mean.
Central Limit Theorem: A statistical theory stating that, given a sufficiently large sample size, the sampling distribution of the sample mean will approximate a normal distribution regardless of the original population's distribution.
