Emperical Rule

Emperical Rule - The Empirical Rule Sometimes the...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
1 The Empirical Rule Sometimes the distribution is symmetric and bell shaped. For these kind of distribution mean and sd together can describe the distribution fairly well. Most of the observations lie near the center or mean of the data. EMPIRICAL RULE summarizes the distribution
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 The Empirical Rule For data with a bell-shaped distribution Approximately 68% of the observations will be within ONE STANDARD DEVIATION of the mean. mean 68%
Background image of page 2
3 Two Standard Deviations For data having a bell-shaped distribution Approximately 95% of the data values will be within TWO STANDARD DEVIATION of the mean. 2 SD 2 SD mean 95%
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Three Standard Deviations For data having a bell-shaped distribution Approximately 99.7% of the data values will be within THREE STANDARD DEVIATION of the mean. mean 3 SD 3 SD
Background image of page 4
5 Chebyshev’s Rule Applies to any distribution More general but less “precise” It says that for any number k > 1 , at least (1-1/k 2 ) fraction of the data will lie within k standard deviations of mean.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 Different k’s 1-1/3 2 = 0.89 1-1/2 2 = 0.75 Distance from the Mean Minimum Proportion of Values Falling Within Distance Number of Standard Deviations k = 2 k = 3 k = 4 1-1/4 2 = 0.94
Background image of page 6
Example 8.0 (Empirical Rule) In a large class of 500 students mean score is 84 and the standard deviation is 5. Suppose the distribution is bell shaped. Then by empirical rule: Approximately 68% of the students got between 79 and 89 Approximately 95% of the students will have score between 74 and 94 Approximately 99.7% of the students will get between 69 and 99
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 28

Emperical Rule - The Empirical Rule Sometimes the...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online