Measures of Central Tendency- Biostatistics - Ravinandan A P.pdf

Measures Describing
The Central Tendency Distributions- Average, Median, Mode, Biostatistics

1. Measures Describing
The Central Tendency
Distributions-
➢Average,
➢Median,
➢Mode
Ravinandan A P
Assistant Professor
Sree Siddaganga College of Pharmacy
In association with
Siddaganga Hospital
Tumkur-02

2. Measures of Central Tendency
•Thetendencyofstatisticaldatatogetconcentratedatcertain
valuesiscalledthe“CentralTendency”
•Thevariousmethodsofdeterminingtheactualvalueat
whichthedatatendtoconcentratearecalledmeasuresof
centralTendencyoraverages.
•Hence,anaverageisavaluewhichtendstosumupor
describethemassofthedata.

3. The Arithmetic Mean or simple Mean
•The arithmetic mean is the sum of all observations divided by the number
of observations. mean ; it is usually denoted by .
•Suppose the sample consists of birth weights (in grams) of all live born
infants born at a private hospital in a city, during a 1-week period.
•This sample is shown in the following table:
3265 3323 2581 2759 3260 3649 2841
3248 3245 3200 3609 3314 3484 3031
2838 3101 4146 2069 3541 2834

4. •It is written in statistical terms as:

5. •Thearithmeticmeanis,ingeneral,averynaturalmeasureof
centrallocation.
•Oneofitsprincipallimitations,however,isthatitisoverly
sensitivetoextremevalues.
•Inthisinstanceitmaynotberepresentativeofthelocation
ofthegreatmajorityofthesamplepoints.

6. •Forex,ifthe1
st
infantwereintheabovedatahappenedtobea
prematureinfantweighing500gmratherthan3265g,thenthe
arithmeticmeanofthesamplewouldbereducedto3028.7g.
•Inthisinstance,7ofthebirthweightswouldbelowerthearithmetic
mean,&13wouldbehigherthanthemean.
•Itispossibleinextremecasesforallbutoneofthesamplepointsto
beononesideofthearithmeticmean.
•Thearithmeticmeanisapoormeasureofcentrallocationinthese
typesofsample,sinceitdoesnotreflectthecenterofsample.
•Nevertheless,thearithmeticmeanisbyfarthemostwidelyusedmeasure
ofcentrallocation.

7. •Merits of Mean:
✓It is a measure that can be calculated and is unique.
✓It is uses all the observations.
✓It is useful for performing statistical procedures such as comparing the
means from several data groups.
•Demerits of Mean:
✓Itcan notbe representing as graphically.
✓Itcan notdealing with qualitative data, such as cleverness, humanity.
✓It will be wrong mean, if any of the observation missing or dropped.
✓If extreme class in open, it is hard to calculate.

8. Median
•Themedianisthemiddleofadistribution:
•halfthescoresareabovethemedianandhalfarebelowthemedian.
•Themedianislesssensitivetoextremescoresthanthemean&this
makesitabettermeasurethanthemeanforhighlyskeweddistributions.
•Themedianincomeisusuallymoreinformativethanthemeanincome,
forexample.
•Thesumoftheabsolutedeviationsofeachnumberfromthemedianis
lowerthanisthesumofabsolutedeviationsfromanyothernumber.
•MedianisdenotedbythesymbolofM.

9. Eg:-3,4,4,5,6, 8,8,8 and 10 has median 6
5,5,7,9,11,12,15 & 18 has Median=9+11/2=10

11. •Merits of Median:
- It is very easy to calculate.
- It is rigidly defined.
- It is affected by the extreme values but is affected by the middle one or
two values.
- It can be calculated with open-end classes.
•Demerits of Median:
- If series has many observations, then it is very cumbersome to
calculate.
- It is not using all the observations.
When dealings with even number of observations, it involves only the mean
of two middle terms.

12. Mode
•Thestatisticalmodeisthenumberthatoccursmostfrequentlyina
setofnumbers.
•ModeisdenotedbythesymbolofZ.
Tofindthemodeofagroupofnumbers:
-Arrangethenumbersinorderbysize.
-Determinethenumberofinstancesofeachnumericalvalue.
-Thenumericalvaluethathasthemostinstancesisthemode.
-Theremaybemorethanonemodewhentwoormorenumbers
haveanequalnumberofinstancesandthisisalsothemaximum
instances
-Amodedoesnotexistifnonumberhasmorethanoneinstance.

13. •The mode is not often used in biological or medical data.
•Find the modal values for the following data
a) 22, 66, 69, 70, 73. (no modal value)
b) 1.8, 3.0, 3.3, 2.8, 2.9, 3.6, 3.0, 1.9, 3.2, 3.5 (modal value = 3.0 kg)

14. •Merits of Mode:
•The mode is not unduly affected by extreme values.
•Most frequent value of the data set to be modal value.
•It is easy to calculate.
•Demerits of Mode:
•It is difficult to find a clearly defined mode.
•It is not based upon all the observations.
•There is no modal value, because the data set contains no values that occur
more than once.
•It is very difficult to interpret and compare, when data sets contain two,
three or many modes.

15. Thank you