measuresofcentraltendency-120205183125-phpapp02

8/15/2019 measuresofcentraltendency-120205183125-phpapp02

1/19

Measures of CentralTendency

Mean, Median and Modefor Ungrouped DataBasic Statistics


2/19

Measures of CentralTendency

In layman’s term, ameasure of central tendencyis an AVERAGE . It is a singlenumber of value which canbe considered typical in a setof data as a whole.

or e!ample, in a class of"# students, the averageheight would be the typicalheight of the members of thisclass as a whole.

Measures of central tendency are numerical

descriptive measures which indicate or

locate the center of a distribution or data

set.


3/19

MEAN

Among the three measures of centraltendency, the mean is the most popular andwidely used. It is sometimes called the arithmeticmean.

If we compute the mean of the population, wecall it the parametric or population mean, denotedby μ (read “mu”).

If we g et the m ean of the s ample, we cal l it thesample mean and it is denoted by (read “x bar”).

$he MEAN of a set of values or measurements isthe sum of all the measurements divided by thenumber of measurements in the set.


4/19


5/19

Your turn!

Mang John is a meat vendor. The following are his sales forthe past six days. Compute his daily mean sales.

Tuesday P !""#ednesday ! $""Thursday $ ""Friday % &""

'aturday () ""'unday (& %""

'olution*

= (, (""

The average daily sales of Mang John is P (,("".


6/19

Weighted Mean

#eighted mean is the mean of a set of values whereinea+h value or measurement has a different weight or

degree of importan+e. The following is its formula*

where = mean

x = measurement or value

w = number of measurements


7/19

Exampleelow are -maya s sub/e+ts and the +orresponding number

of units and grades she got for the previous grading

period. Compute her grade point average.

Subject Units rade

Filipino .0 !$

1nglish (. !

Mathemati+s (. !!'+ien+e (.! !2

'o+ial 'tudies .0 !$

T31 (.) !&

M-P14 (.) !2

= !$.(

-maya s average grade is !$.(


8/19

Your turn!James obtained the following grades in his five sub/e+ts forthe se+ond grading period. Compute his grade point average.

'olution*

= !2.$2

James general average is !2.$2

Subject Units rade

Math (. 0"

1nglish (. !$

'+ien+e (.! !!

Filipino ".0 !2

M-5- -6-7 (. !2


9/19

i ert"type #uestion

-e!t are e!amples of i/ert0type statements.

Respondents will choose the number which bestrepresents their feeling regarding the statements.-ote that the statements are grouped accordingto a theme.

This is used if the resear+her wants to 8now the feelings oropinions of the respondents regarding any topi+ or issues ofinterest.

!hoices

9'-: 'trongly -gree% 9-: -gree

& 97: 7eutral

) 9;: ;isagree

( 9';: 'trongly ;isagree


10/19

Students" persona# confidence in #earningStatistics

5 $ 3 % &

(. < am sure that < +an learn 'tatisti+s

). < thin8 < +an handle diffi+ult lessons in'tatisti+s.

&. < +an get good grades in 'tatisti+s.

Source: B.E. Blay, Elementary Statistics

elow are the responses in the 3i8ert type ofstatements above. The table below shows the meanresponses and their interpretation. >sing the formula for+omputing the weighted mean, +he+8 the +orre+tness of thegiven means on the table.

5 $ 3 % & Mean 'nterpretation

( &$ ( (! " ( %.(% -gree

) (! %% &2 ! ( &.$ -gree

& (! %! )! " ( &.!$ -gree


11/19

i ert"type Mean$nterpretation

(." (.20 'trongly ;isagree(.! ). 0 ;isagree

).$ &.&0 7eutral

&.% %.(0 -gree

%.) ."" 'trongly -gree


12/19

Your turn!elow is the result of the responses to the following 3i8ert

type statements . 'olve for the mean and give the

interpretation.

5 $ 3 % & Mean 'nterpretation

( && %0 )$ ( (

) & % &( " (

& &% ! )( " "

Students" perception on Statistics as asubject

5 $ 3 % &

(. < thin8 'tatisti+s is a worthwhile, ne+essarysub/e+t

). < will use 'tatisti+s in many ways as aprofessional

&. < ll need a good understanding of 'tatisti+sfor my resear+h wor8


13/19

%roperties of Mean

(. Mean +an be +al+ulated for any set ofnumeri+al data, so it always exists.

). - set of numeri+al data has one and only onemean.

&. Mean is the most reliable measure of +entraltenden+y sin+e it ta8es into a++ount every itemin the set of data.

%.


14/19


15/19

Your turn!

Compute the median and interpret the result.(.


16/19

%roperties of Median

(. Median is the s+ore or +lass in the distributionwherein "@ of the s+ore fall below it andanother "@ lie.

). Median is not affe+ted by extreme or deviant

values.&. Median is appropriate to use when there are

extreme or deviant values.

%. Median is used when the data are ordinal.

. Median exists in both Auantitative or Aualitativedata.


17/19

M'DE $he M'DE& denoted %o & is the value which

occurs most fre2uently in a set of measurements or

values. In other words, it is the most popular value

in a given set.

1xamples*Find the Mode.(. The ages of five students are* (2, (!, )&, )", and (0). The following are the des+riptive evaluations of

tea+hers* B', ', B', B', &. The grades of five students are * %.", &. , %.", &. , and

(."%. The weights of five boys in pounds are* ((2, )(!, )&&,

()", and ((2


18/19

%roperties

(.


19/19

Documents

measuresofcentraltendency-120205183125-phpapp02