Quartiles The value which divide the arranged data into four equal parts are called Quartiles. These values are denoted by Q1, Q2, and Q3. Where Q1= The first quartile Q2= The second quartile Q3= The third quartile
Quartiles for ungroupd data n+1 Q 1 = first Quartile=( )th value 4 n+1 Q 2=Second Quartile=2( )th value 4 n+1 Q 3 =Third Quartile=3( )th value 4 Q. Find all quartiles for the following data? 2,3,3,9,6,6,12,11,8,2,3,5,7,5,4,4,5,12,9
Quartiles for ungroupd frequency distribution f +1 ∑ Q =First Quartile=( )th value 1
4
f +1 ∑ Q =Second Quartile=2( )th value 2
4
f +1 ∑ Q =Third Quartile=3( )th value 3
4
Q. Find all the quartiles from the following ungrouped frequency distribution. Marks
0
1
2
3
4
5
6
7
8
9
10
Frequency
2
2
3
4
6
11
15
10
6
3
1
Quartiles for Grouped frequency distribution h ∑f Q 1= First Quartile=l+ ( −C.f.) f 4 h 2∑ f Q 2=Second Quartile=l+ ( −C.f.) f 4 h 3∑ f Q 3 =Third Quartile=l+ ( −C.f.) f 4 Wages in Rs. No. of Workers
150-170
170-190
190-210
210-230
230-250
30
50
80
30
10
Deciles The values that divides the data into ten (10) equal parts are called deciles. These values are denoted by D1 = First Decile D2 = Second Decile …............................ …............................ …............................ D9 = Ninth Decile
Deciles for upgrouped data n+1 D 1=First Decile=( )th value 10 n+1 D 2=Second Decile=2( )th value 10 n+1 D 3=Third Decile=3( )th value 10 .......................................................... .......................................................... n+1 D 9=Ninth Decile=9( )th value 10 Q. Find fouth Decile (D4) and sixth Decile (D6) for the following date. 19,27,24,39,57,44,56,50,59,67,62,42,47,60,26,34,57,51,59,45
Deciles for ungrouped frequency distribution f +1 ∑ D =First Decile=( )th value 1
10
f +1 ∑ D =Second Decile=2( )th value 2
10 f +1 ∑ D 3=Third Decile=3( )th value 10 ........................................................ f +1 ∑ D 9=Ninth Decile=9( )th value 10
Q. Fine D2 and D6 from the following data. x f
4 2
5 4
6 13
7 35
8 51
9 54
10 69
11 41
12 27
13 54
Deciles for Grouped frequency distribution h ∑f D 1=First Decile=l+ ( −C.f.) f 10 h 2∑ f D 2=Second Decile=l+ ( −C.f.) f 10 h 3∑ f D 3=Third Decile=l+ ( −C.f.) f 10 ................................................... h 9∑ f D 9=Ninth Decile=l+ ( −C.f.) f 10 Q. Fine D2 and D3 from the following data? x f
0-5 7
5-10 18
10-15 25
15-20 30
20-25 20
Percentiles The values which divide the arranged data into hundred (100) equal parts are called percentiles. These values are denoted by P1=First Percentile P2=Second Percentile …................................. …................................. P99=99th Percentile
Percentile for ungrouped data n+1 P 1=First Percentile=( )th value 100 n+1 P 2=Second Percentile=2( )th value 100 n+1 P 3=Third Percentile=3( )th value 100 ...................................................... n+1 P 99 =99th Percentile=99( )th value 100
Percentile for ungrouped frequency distribution f +1 ∑ P =First Percentile=( )th value 1
100 f +1 ∑ P 2=Second Percentile=2( )th value 100 f +1 ∑ P 3=Third Percentile=3( )th value 100 ...................................................... f +1 ∑ P 99 =99th Percentile=99( )th value 100 Q. Find P10, P40, P90 from the following data? x f
100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 3 6 10 15 24 42 75 90 79 55 36 26 19 13 8
Percentile for grouped frequency distribution h ∑f P 1=First Percentile=l + ( −C.f.) f 100 h 2∑ f P 2=Second Percentile=l+ ( −C.f.) f 100 h 3∑ f P 3=Third Percentile=l+ ( −C.f.) f 100 ............................................. h 99 ∑ f P 99 =99th Percentile=l+ ( −C.f.) f 100 Q. Find P20, P60 and P75 from the following data? x f
2-12 2
12-22 22-32 32-42 42-52 52-62 62-72 72-82 82-92 92-102 5 8 12 15 20 16 14 10 8
