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Measures of Center Tendency

What Is Measures of Center Tendency?

Measures of central tendency are numerical descriptive measures

which indicate or locate the center of a distribution or data set.

Types of Measures of Tendency :

Mean Meiden Mode

Arithmetic Mean Geometric Mean Weighted Mean

Mean

What Is Mean?

The Mean of a set of values or

measurements is the sum of all the

measurements divided by the number of

measurements in the set.

Arithmetic Mean

The arithmetic mean is the sum of a set of

observations,

positive, negative or zero, divided by the number

of observations.

Arithmetic Formula of MEAN

n

xx

n

in

1

Arithmetic Example

An electronics store sells CD players

at the following prices:

$350, $275, $500, $325, $100, $375, and $300.

What is the mean price?

$2225 / 7 = $317.86

The mean or average price of a CD player is $317.86.

What is Geometric Mean ?

The Geometric Mean is a special type of average

where we multiply the numbers together and then

take a square root (for two numbers), cube root

(for three numbers) etc.

Formula of Geometric Mean

n√(a1 × a2 × ... × an)

What is Weighted Mean ?

The weighted mean is a special case of arithmetic

mean. It occurs when there are several

observations of the same value.

Formula of Weighted Mean

n

ii

n

iii

w

xwx

1

1

Meiden

What Is Meiden ?

The Median is the middle value of a set of data.

Formula of Meiden (Ungroup) :

)1(2

1

n

e XMFor odd

1222

1nne XXMFor even

Formula of Meiden (group) :

Fn

f

iLM

ooe 2

Lower class boundary of the median Class

class interval

Frequency of the median class Cumulative

frequency

Mode

What is Mode ?

The Mode is the most frequently observed value in a data set.

Formula of Mode:

iLM

21

110

Slope Angle (°)

Frequency (f)

0-5 6

5-10 12

10-15 7

15-20 5

20-25 0

0Li

1

2

= Lower class boundary of modal class = Interval of modal class

= difference of frequency of modal class and class before modal class

= difference of frequency of modal class and class after modal class

0L

modal class which has highest frequency

Example :

The most frequently printed words in English are: the, of, and, a , and to.

ANY QUESTION ?

THANK YOU !!