P2.2. Summary Measures Flashcards
compressing mass of data for better comprehension and description
Summary measures
3 Category of Summary Measures:
- measures of central tendency
- measure of dispersion
- measures of location
refers to “center” of the distribution of observations
three most common measures?
Measures of Central Tendency
- mean
- median
- mode
also known as average
(Arithmetic) MEAN
- sensitive to extreme observations [outliers]
- involves all observation in its computation
- any change in the observation will change the mean value
- calculated for any quantitative variable
* unit is the same as that of the original set of observations
(Arithmetic) MEAN
-
sum of the deviations of the observations from the mean is equal to zero
[point of balance or center of gravity of the distribution] - serves as basis for the computation of higher statistical methods
(Arithmetic) MEAN
middle most value in a set of observations put in an array
MEDIAN
- always exists and is unique
- not influence by outliers
- does not make use of all the observations in its computation
- can be calculated for any quantitative variable
- can be calculated for some qualitative variable
MEDIAN
- most frequently occurring value in a set of observation
- no calculations needed
- determined for any type of variable
it is possible to have:
* no mode
* unimodal; bimodal; multimodal
MODE
- gives information as to the tendency of values to clump together
- tools describing the variability of the observations: HOMOGENOUS & HETEROGENOUS
- may be used for quantitative variables only
four most common measures?
Measures of Dispersion
- range
- variance
- standard deviation
- coefficient variation
- simplest measure of location
- highest observation – lowest observation
- does not tell anything about the observation between these two extreme observations
- may be used for quantitative variables
no observations given.
RANGE
- measure of variability that takes the mean as the reference point
- involves all observations
- unit: squared unit of the original set of observations
- hard to interpret
no observations given.
VARIANCE
- square root of variance
- unit is the same as that of the original set of observations
STANDARD DEVIATION
* expresses the SD as percentage of mean
most appropriate when:
* unit of measurement of variables being compared are different
* *means being compared are markedly different *
COEFFICIENT VARIATION
measure of dispersion is low or small
homogenous distribution of observation
measure of dispersion is high or large
heterogenous distribution of observation
- determines the location/ position of particular value in an array of distribution
- provide more details about a part of the entire distribution of observations in a given data
- used for both qualitative and quantitative data
three most common measures?
Measures of Location
- quartiles
- deciles
- percentiles
points of distribution that divides the observation into 4 equal parts
QUARTILES
points of distribution that divides the observation into 10 equal parts
DECILES
points of distribution that divides the observation into 100 equal parts
PERCENTILES
- calculated by dividing the cumulative frequency by the total no. of observations (n)
- then multiply it by 100
CUMULATIVE PERCENTAGE
To find the value of particular percentile, refer to the cumulative percentage equal to or higher than the percentile in question
