Elementary Statistics and Computer Application

Quartiles

• The quartiles divide the distribution in four parts. There are three quartiles. The second quartile divides the distribution into two halves and therefore is the same as the median. The first (lower).quartile (Q1) marks off the first one-fourth, the third (upper) quartile (Q3) marks off the three-fourth. It may be noted that the second quartile is the value of the median and 50th percentile.

Raw or ungrouped data

• First arrange the given data in the increasing order and use the formula for Q1 and Q3 then quartile deviation, Q.D is given by

Where item and item

Example 18

• Compute quartiles for the data given below (grains/panicles) 25,18,30, 8, 15, 5, 10, 35, 40, 45

Solution
5, 8, 10, 15, 18,25, 30,35,40, 45


= (2.75)th item
= 2nd item + (3rd item – 2nd item)
= 8+ (10-8)
= 8+ x 2
= 8+1.5
= 9.5

= 3 x (2.75)th item
= (8.75)th item
= 8th item + (9th item – 8th item)
= 35+ (40-35)
= 35+1.25
= 36.25

Discrete Series
Step1: Find cumulative frequencies.
Step2: Find
Step3: See in the cumulative frequencies , the value just greater than , then the corresponding value of x is Q1
Step4: Find
Step5: See in the cumulative frequencies, the value just greater than ,then the corresponding value of x is Q3

Example 19
Compute quartiles for the data given bellow(insects/plant).

X	5	8	12	15	19	24	30
f	4	3	2	4	5	2	4


Solution
x	f	cf
5	4	4
8	3	7
12	2	9
15	4	13
19	5	18
24	2	20



=18.75th item .^..Q1= 8; Q3=24
Continuous series
Step1: Find cumulative frequencies
Step2: Find
Step3: See in the cumulative frequencies, the value just greater than , then the corresponding class interval is called first quartile class.
Step4: Find See in the cumulative frequencies the value just greater than then the corresponding class interval is called 3rd quartile class. Then apply the respective formulae


Where l1 = lower limit of the first quartile class

• f1 = frequency of the first quartile class
• c1 = width of the first quartile class
• m1 = c.f. preceding the first quartile class
• l3 = 1ower limit of the 3rd quartile class
• f3 = frequency of the 3rd quartile class
• c3 = width of the 3rd quartile class
• m3 = c.f. preceding the 3rd quartile class

Example 20:

The following series relates to the marks secured by students in an examination

Marks	No. of Students
0-10	11
10-20	18
20-30	25
30-40	28
40-50	30
50-60	33
60-70	22
70-80	15
80-90	12
90-100	10

Solution

C.I	f	cf
0-10	11	11
10-20	18	29
20-30	25	54
30-40	28	82
40-50	30	112
50-60	33	145
60-70	22	167
70-80	15	182
80-90	12	194
90-100	10	204
	204