(4)Sec2.4-2.6

# (4)Sec2.4-2.6 - Continued from Order Statistics Explanation...

This preview shows pages 1–6. Sign up to view the full content.

Continued from Order Statistics

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

View Full Document
Explanation of Quantiles We are given a data set as the sample, 1 st Quartile, Q 1 , is the 25% quantile which means 25% of the data from the sample will be less than or equal Q 1 , Median, M e , is the 50% quantile which means half of the data from the sample will be less than or equal M e , 3 rd Quartile, Q 3 , is the 75% quantile which means 75% of the data from the sample will be less than or equal Q 3 ,
Similarly, 90% quantile, Q 0.9 means 90% of the data from the sample will be less than or equal Q 0.9 . In general, for any percentage p, 0<p<1, p th quantile Q p means 100p% of the data from the sample will be less than or equal Q p . So we develop the formula based on this definition for quantiles as following: Q p =X ([K]) +{K}(X ([k]+1) – X ([K]) ) where K=(n+1)p, 0<p<1, and [K] is the integer part of number K and {K} is the fractional part of the number K, so {K}=K-[K].

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

View Full Document
Quantile of X Percent 6 5 4 3 2 1 100 80 60 40 20 0 50% 90% 25% 75% Q1 Me Q3 Qp, p=90% Empirical CDF of 2.4016
Dispersion which is a useful measure of dispersion when there are outliers in the sample. which is a dimensionless index used to compare the variability

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 24

(4)Sec2.4-2.6 - Continued from Order Statistics Explanation...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online