Statistics - Paper 2 - For Class ICOM - Part 2 (Commerce Group) - Complete Solved Model Paper With Solved MCQs 2020 -2021

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Statistics- Paper 2
For Class XII (Commerce Group)
Solved Model papers 2020 -2021

Time: 50 Minutes    Max. Marks: 25

SECTION "B" (SHORT - ANSWER QUESTIONS) (15 Marks)

Q. No.2 Attempt any Three part questions. All questions carry equal marks.

(i) Differentiate between Primary data and Secondary data Or Define Discrete and Continuous variables with examples.
SOLUTION 2 (i):

DIFFERENCE BETWEEN PRIMARY DATA AND SECONDARY DATA

Primary Data	Secondary Data
Primary data are original in nature.	Secondary data are not in original in nature.
Primary data is collected systematically therefore, suitability of primary data is positive.	Suitability of secondary data may or may not be positive.
It is time consuming and expensive.	Secondary data are cheaper than primary data.
Primary data does not require extra precautions.	Secondary data require great care and cautions.
Primary data are in the shape of raw material.	Secondary data are in the shape of finished products.

OR

Discrete Variable:
A discrete variable is a variable whose value is obtained by counting.
Examples:

1. Number of students present.
2. Number of red marbles in a jar.

Continuous Variable:
A continuous variable is a variable whose value is obtained by measuring.
Examples:

1. Height of students in class.
2. Weight of students in class.

(ii) Find relative frequency distribution and cumulative frequency distribution to the following distribution:

C.I.	2 -- 4	5 -- 7	8 -- 10	11 -- 13	14 -- 16
F	1	3	4	5	2

SOLUTION 2 (ii)

Class Interval	Frequency	Relative Frequency	Cumulative Frequency
2 - 4 5 - 7 8-10 11 - 13 14 - 16	1 3 4 5 2	1/15 = 0.067 3/15 = 0.200 4/15 = 0.267 5/15 = 0.333 2/15 = 0.133	1 1 + 3 =4 4 + 4=8 8 + 5 =13 13+2=15
	∑f = 15	1.000

(iii) Represent the following data by a Pie diagram.

Items	A	B	C	D	E
Expenditure (Rs.)	50	30	20	15	35

SOLUTION 2 (iii)

Items	Expenditure	Degree
A	50	50/150 x 360 = 120°
B	30	30/150 x 360 = 72°
C	20	20/150 x 360 = 48°
D	15	15/150 x 360 = 36°
E	35	35/150 x 360 = 84°
Total	150	360°

(iv) Find median for the following data:

C.I.	2	3	4	5	6	7
F	7	11	16	20	22	24

SOLUTION 2 (iv)

Class Interval	Frequency	Cumulative Frequency
2	7	7
3	11	7 + 11 = 18
4	16	18 + 16 = 34
5	20	34 + 20 = 54
6	22	54 + 22 = 76
7	24	76 + 24 = 100
	∑f = 100

(v) From the data given below, calculate the index number of prices for 1991 with reference to 1990 as the base year, using Simple Aggregative Method.

Commodity	Year
	1990	1991
A	3	5
B	10	15
C	2	4

SOLUTION 2 (v)

Commodity	Po	Pn
A	3	5
B	10	15
C	2	4
Total	15	24

OR

(v) A bag contains 3 Red and 4 Black balls. 2 balls are drawn at random from the bag. Whet is the probability that the balls are one of each colour?
SOLUTION 2 (v):
n = 7
r = 2

SECTION "C" (DETAILED - ANSWER QUESTIONS)
(10 Marks)

Note: Answer any one question from this section. All question carry equal marks.
Q. No.3 (a): Find Arithmetic mean and Mode for the following frequency distribution.
SOLUTION 3 (a)

C.I.	F	X	Fx	C - B	CF
2 - 4	2	(2 + 4)/2 = 3	2 x 3 = 6	1.5 - 4.5	2
5 - 7	8	(5 + 7)/2 = 6	8 x 6 = 48	4.5 - 7.5	2 + 8 = 10
8 - 10	12	(8 + 10)/2 = 9	12 x 9 =108	7.5 - 10.5	10 + 12 = 22
11 - 13	4	(11 + 13)/2 = 12	4 x 12 = 48	10.5 - 13.5	22 + 4 = 26
14 - 16	2	(14 + 16)/2 = 15	2 x 15 = 30	13.5 - 16.5	26 + 2 = 28
	∑f = 28		∑fx = 474

Q, No.3 (b): Given that event A and B are mutually exclusive events such that P(A) = 0.3, P(B) = 0.6; Find P(AUB).
SOLUTION 3 (b):
P(AUB) = P(A) + P(B)
P(AUB) = 0.3 + 0.6
P(AUB) = 0.9 Ans.

Q. No.4 (a): Calculate Laspeyre's and Paasche's price index numbers for 1991 using 1990 as base year:

Commodity	1990		1991
	Price	Quantity	Price	Quantity
A	10	4	12	3
B	6	5	9	2
C	5	3	8	1

SOLUTION 4 (a):

Commodity	Po	qo	Pn	qn	Pnqo	Poqo	Pnqn	Poqn
A	10	4	12	3	48	40	36	30
B	6	5	9	2	45	30	18	12
C	5	3	8	1	24	15	8	5
					117	85	62	47

Q. No.4 (b): Two dice are rolled once. Construct the Sample Space. What Is the probabiltty of getting a total of:
(a) 9?
(b) 7 Or 11

SOLUTION 4(b):

SOURCE: Board Of Intermediate Education Karachi