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# five number summary in statistics

From Wikipedia

Summary statistic

In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible. Statisticians commonly try to describe the observations in

A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.

Entries in an analysis of variance table can also be regarded as summary statistics.

## Example

The following example using R is the standard summary statistics of a randomly sampled normal distribution, with a mean of 0, standard deviation of 1, and a population of 50: > x <- rnorm(n=50, mean=0, sd=1) > summary(x)Min. 1st Qu. Median Mean 3rd Qu. Max. -1.72700 -0.49650 -0.05157 0.07981 0.67640 2.46700

## Examples of summary statistics

### Location

Common measures of location, or central tendency, are the arithmetic mean, median, mode, and interquartile mean.

Common measures of statistical dispersion are the standard deviation, variance, range, interquartile range, absolute deviation and the distance standard deviation. Measures that assess spread in comparison to the typical size of data values include the coefficient of variation.

The Gini coefficient was originally developed to measure income inequality and is equivalent to one of the L-moments.

### Shape

Common measures of the shape of a distribution are skewness or kurtosis, while alternatives can be based on L-moments. A different measure is the Distance skewness, for which a value of zero implies central symmetry.

### Percentiles

A simple summary of a dataset is sometimes given by quoting particular order statistics as approximations to selected percentiles of a distribution.

### Dependence

The common measure of dependence between paired random variables is the Pearson product-moment correlation coefficient, while a common alternative summary statistic is Spearman's rank correlation coefficient. Distance correlation equals zero implies independence.

Five-number summary - Wikipedia, the free encyclopedia

The five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the five most important sample ...

Question:im trying to study, it has questions and answers. but i need to get it order to pass my test. it says What is the five-number summary for the data? what does that mean?

Answers:In descriptive statistics, the five-number summary of a data set consists of: the minimum (smallest observation) the lower quartile or first quartile (which cuts off the lowest 25% of the data) the median (middle value) the upper quartile or third quartile (which cuts off the highest 25% of the data) the maximum (largest observation) hope this helps

Question:I just started taking statistics, but I was wondering if negative numbers in a five number summary is normal. It seems a little strange to me considering that the data that it is for (the number of items memorized by students) cannot ever be a negative number. So, are negative numbers normal or should I redo my calculations?

Answers:If your data set is strictly positive then all the values in the five number summary, the minimum, first quartile, median, third quartile and maximum, are all going to be positive values as well. If you have negative values then there is a major mistake in your calculations.

Question:Here's the five-number summary for the distribution of cigarette taxes (in cents) among the 50 states in the United States. Minimum = 2.5 Q1 = 36 Median = 60 Q3 = 100 Maximum = 205 a. About what proportion of the states have cigarette taxes (i) greater than 36 cents, (ii) greater than \$1? b. Between what two values are the middle 50% of the observations found? c. Find the interquartile range. Interpret it. d. Based on the summary, do you think that this distribution was bell shaped? If so, why? If not, why not, and what shape would you expect?

Answers:the first quartile is the value for which 25% of the data is less than this value, the median is 50% and the third quartile is the point with 75% of the data having a lower value. ai) 75% (36 cents is the first quartile) aii) 100% (no state has a tax lower than the minimum of 2.5 cents b) the middle fifty percent of the data is between the third and first quartile. this is also called the inner quartile range. c) the inner quartile range is Q3 - Q1 = 64 d) not bell shaped, the distance between the median and the quartiles is not even (24 cents on the lower end vs 40 on the upper end) and there for the data is not symmetric and not bell shaped.

Question:Does an outlier mean more than one thing in statistics?

Answers:i know its the number that stands out in a number group... thats the only one i know of.