6 Marks Question

Question

Calculate quartile deviation and its coefficient from the following data 139, 140, 140, 141, 141, 142, 142, 143, 143, 144, 144, 145

Vidyadip · Accepted Answer

Calculation of Quartile Deviation and Coefficient of Quartile Deviation:

S. No.	X
1	139
2	140
3	140
4	141
5	141
6	142
7	142
8	143
9	143
10	144
11	144
12	145

$Q_1$ = Size of $\Big(\frac{\text{n}+1}{4}\Big)^\text{th}\text{ item}$ = Size of $\Big(\frac{12+1}{4}\Big)^{\text{th}}\text{item}$ = Size of $\Big(\frac{13}{4}\Big)^{\text{th}}\text{item}$ = Size of 3. $25^{th}$ item = Size of 3rd item + 0.25(4th item - 3rd item) = 140 + 0.25(141 - 140) = 149.25 $Q_3$ = Size of $3\Big(\frac{\text{n}+1}{4}\Big)^{\text{th}}\text{item}$ = Size of $3\Big(\frac{12+1}{4}\Big)^{\text{th}}\text{item}$ = Size of $9.75^{th}$ item = Size of $9^{th}$ item $+ 0.75 (10^{th}$ item - $9^{th}$ item) = 143 + 015 (144 - 143) = 143.75 Now, QD $=\frac{\text{Q}_3-\text{Q}_1}{2}$$=\frac{143.75-140.25}{2}=1.75$
Coefficient of QD $=\frac{\text{Q}_3-\text{Q}_1}{\text{Q}_3+\text{Q}_1}$$=\frac{143.75-140.25}{143.75+140.25}$
$=\frac{3.5}{284}=0.012$

Wages (in ₹)	Number of Workers (f)
0-10	10
10-20	18
20-30	35
30-40	30
40-50	20
50-60	12
60-70	8
70-80	3

Marks obtained:	140-150	150-160	160-170	170-180	180-190	190-200
No. of girls:	4	6	10	18	9	3

Class lnterval	Frequency (f)
17.5-22.5	2
22.5-27.5	4
27.5-32.5	6
32.5-37.5	8
37.5-42.5	6
42.5-47.5	4
47.5-52.5	2
52.5-57.5	2

Marks:	30-35	35-40	40-45	45-50	50-55	55-60	60-65
No. of Students:	14	16	18	23	18	8	3

Weekly wages (in ₹)	Number of Woekers
10-15	7
15-20	10
20-25	27
25-30	15
30-40	12
40-60	12
60-80	8

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