ap stats study guides

โœŒ๏ธย  Unit 2 - Exploring Two-Variable Data

โš–๏ธย  Unit 6 - Inference for Categorical Data: Proportions

๐Ÿ˜ผย  Unit 7 - Inference for Qualitative Data: Means

โœณ๏ธย  Unit 8 Inference for Categorical Data: Chi-Square

๐Ÿ“ˆย  Unit 9 - Inference for Quantitative Data: Slopes

๐Ÿงย  Multiple Choice Questions (MCQs)

5.2 The Normal Distribution, Revisited

#exploringdata

#sampling

#experimentation

#anticipatingpatterns

#statisticalinference

โฑ๏ธย ย 2 min read

written by

Josh Argo

josh argo

brianna bukowski

Harrison Burnside

harrison burnside

(editor)


Definition

A normal model is unimodal (one mound, bell-shaped) and symmetric. The median and mean are equal to each other.

When asked to describe a normal model, talk about the center, shape, and spread.

Furthermore, a model (such as a sampling distribution) is approximately normal if the following conditions are met for the following types of data:

Categorical (Proportions)

Quantitative (Means)

  • The number of successes and failures is at least 10 (Large Counts)

  • The sample size is at least 30 (Central Limit Theorem which youโ€™ll learn about in the next post)

OR

  • Population is normally distributed

Empirical Rule Review

The area underneath any density curve (including the normal curve) is equal to 1, or 100% of the data. There is 50% of the data on each size of the mean.

  • 68% of the data is within 1 standard deviation of the mean. (34% on each side)

  • 95% of the data is within 2 standard deviations of the mean (an additional 13.5% on each side)

  • 99.7% of the data is within 3 standard deviations of the mean (an additional 2.35% on each side)

https://miro.medium.com/max/24000/1*IdGgdrY_n_9_YfkaCh-dag.png

Source: Medium

๐ŸŽฅWatch: AP Stats - Normal Distributions

A z-score indicates how many standard deviations above or below the mean a piece of data is. If a z-score is -2, it is 2 standard deviations below the mean. If a z-score is 1, it is 1 standard deviation above the mean.ย  When asked to interpret a z-score, it is imperative that you indicate the direction (positive or negative). The magnitude of the z-scores is also important, especially when making inferences.

Z-scores are often used to compare scores regarding two sets of data, like SAT and ACT scores. The z-scores are resistant to units. Therefore the units do not matter and the z-scores remain the same if we convert the units.ย  Think of z-scores as a way of comparing apples ๐ŸŽ to oranges ๐ŸŠ.

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