QUARTILE DEVIATION

In measures of dispersion the first concept is Range which we have completed earlier in previous blog. If you want visit again CLICK HERE => RANGE

Now, we have to start the 2nd topic, Quartile Deviation.

CONCEPT

suppose think there is a number line staring from 0 and ending with 8. Now I asked you divide this number line into 4 equal parts. You may show like this

Q1. Q2 Q3.

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0—–1——2–—3–—4–—5——6–—7–—8

So, you divided like this. There are 4 parts divided by using 3 lines. These lines are named as quartiles. For every 25% area on number line there will be one quartile.

Q1, Q2,Q3 are called quartile.

Ones observe where is median. Yes, Q2 is median.

Here Q1 =2

Q2 = 4

Q3 = 6. This is data of simple numbers so you found it easily. For data with uneven numbers and complex data we will use formulae.

. Q1= 1[ (n+1)/4 ].

Q2= 2[ (n+1)/4 ].

Q3= 3[ (n+1)/4 ]. Where n is number of observations

Individual series

When the data is given in individual series it's very simple to find

Ex:- find quartile deviation for the data 2,10,12,25,15,66,45.

Sol:- Firstly arrange the data in ascending order

AO:- 2,10,12,15,25,45,66.

Number of observations (n) = 7

Now find

Q1 = 1[ (n+1)/4 ] =. 1[ (7+1)/4 ] = 1[ 8/4 ] = 2

So, the Q1 is not 2 but 2nd value in the given series.so, Q1 =10

Q3 = 3[ (n+1)/4 ]. =. 3[ (7+1)/4 ] = 3[ 2]. = 6

So, the Q3 value is not 6 but 6th value in the given series. So, Q3= 45

So Quartile Deviation = (Q3 – Q1)/2

= (45 – 10)/2. =35/2 = 17.5

Discrete series.

It is also same as individual series. But in individual series n means number of observations but here n means sum of frequencies. Let us do an example

Ex:-

X | 2. 4. 6. 8. 10

f | 15 3 6 12 23

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