measures of central tendency, dispersion, location Flashcards
- compressing mass of data for better
comprehension and description.
summary measures
- Refers to “center” of the distribution of
observations.
measures of central tendency
- also known as average
mean
- sensitive to extreme observations.
- involves all observation in its computation.
- any change in the observation will change the mean value.
mean
- middle most value in a set of observations put in an array
- always exists and is unique.
- not influenced by outliers.
- does not make use of all the observations in its
computation. - can be calculated for any quantitative and qualitative variable.
median
most frequently occurring value in a set of observations
mode
- gives information as to the tendency of values to
clump together. - tools describing the variability of the
observations.
measures of dispersion
Simplest measure of location
range
highest observation – lowest observation
range
does not tell anything about the observation between these two extreme observations.
- may be used for quantitative variables
range
Measure of variability that takes the mean as the reference point
variance
- involves all observations.
- unit: squared unit of the original set of observations.
- hard to interpret
variance
- square root of variance
- unit is the same as that of the original set of observations.
sd
square of variance
sd
expresses the SD as percentage of mean.
coefficient variation
most appropriate when unit of measurement of variables being compared are different
coefficient variation
most appropriate when means being compared are markedly different.
coefficient variation
measure of dispersion is low or small.
homogeneous
measure of dispersion is high or large.
heterogenous
determines the location/ position of particular value in an array of distribution
measures of location
- provide more details about a part of the entire distribution of observations in a given data.
- used for both qualitative and quantitative data
measures of location
most common measures:
- quartiles
- deciles
- percentiles
points of distribution that divide the observation into 4 equal parts.
quartiles
points of distribution that divides the observation into 10 equal parts.
deciles
points of distribution that divide the observation into 100 equal parts
percentiles
- calculated by dividing the cumulative frequency by the total number of observations (n).
- then multiply it by 100
cumulative percentage
