key term - Percentile

Definition

A percentile is a measure used in statistics indicating the value below which a given percentage of observations fall. For example, the 50th percentile is the median.

5 Must Know Facts For Your Next Test

1. In the context of sums and distributions, percentiles help understand the variability and spread of data.
2. A percentile can be calculated using the cumulative distribution function (CDF).
3. The 25th percentile is also known as the first quartile, while the 75th percentile is known as the third quartile.
4. In large samples, due to the Central Limit Theorem, percentiles can approximate normal distribution characteristics.
5. Percentiles are particularly useful for summarizing large sets of data points in an easily interpretable manner.

Review Questions

• What does the 90th percentile represent in a dataset?
• How is a percentile related to the cumulative distribution function (CDF)?
• Why are percentiles important when analyzing sums in large datasets?

Related terms

Cumulative Distribution Function (CDF):

A function that represents the probability that a random variable takes on a value less than or equal to a specific value.

Quartile: Values that divide a dataset into four equal parts; includes Q1 (25th percentile), Q2 (50th percentile/median), and Q3 (75th percentile).

Central Limit Theorem:

A statistical theory that states that, given sufficiently large sample size from a population with finite variance, the mean of all samples will be approximately normally distributed.