Measures of variation

Measures of central tendency.

Themodeandthemedian in adiscrete distribution series.

Rule 1. If there are an odd number of values in the data set, the median is themiddle-ranked value.

Rule 2.If there are an even number of values in the data set, the median is theaverage of themiddle-ranked values.

Themodeandthemedian in aninterval distribution series

Themodeof aninterval ofdistribution series:

Themedianof aninterval ofdistribution series:

There is a theoretical rule which says: that a collection is considered to be homogeneous, when there is approximate equality: x ¯ = Mo = Me

Quantiles of distribution

Quantiles of the distribution are characteristic values of a sign that divides a population into equal parts:

The median divides the population into two parts,

The quartile divides the population into four parts

The decile divides the population into ten parts,

The percentile divides the population into a hundred parts.

Quartiles (Q) split a set of data into four equal parts.

Use the following rules to calculate the quartiles:

Rule 1. If the result is a whole number, then the quartile is equal to that ranked value.

Rule 2. If the result is a fractional half (2.5, 4.5, etc.), then the quartile is equal to the average of the corresponding ranked value.

Rule 3. If the result is neither a whole number nor a fractional half, you round the result

The first quartile and the third quartileforungrouped data:

Q1 = (n+1)/4 ranked value,

Q3 = 3(n+1)/4 ranked value.

The first quartile and the third quartileforgrouped data is as follows.

The decile divides the population into ten parts

Percentilelocation value has its own formula for calculations:

i = (p/100)*n

where p is the desired percent,

n – number of values in the data set.

Measures of variation

In international statistics and national statistics the measures of variation are:

range, interquartile range, variance, and standard deviation.

The simplest measure of variation is the range.

R = Xmax. – Xmin.

A measure of variation that helps reduce (decrease) distortion of data because of extreme values is called the interquartile range.

IR = Q3 - Q1,

The population variance is the average of the squared distances of the data values from the mean.

-forungrouped data

-forgrouped data

Simplified methodof calculation of population variance

Thekind of population variance

• The total variance.

• The within - group variance.

• The average of the groupvariance.

• The intergroup variance.

The rule of summing population variance is

The coefficient of determination

Date: 2015-12-24; view: 722