five number summary in statistics
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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 measure of location, or central tendency, such as the arithmetic mean
- a measure of statistical dispersion like the standard deviation
- a measure of the shape of the distribution like skewness or kurtosis
- if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient
Entries in an analysis of variance table can also be regarded as summary statistics.
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
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.
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.
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.
The five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the five most important sample ...
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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
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.
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.
Answers:i know its the number that stands out in a number group... thats the only one i know of.