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11th Business Maths Monthly Test - 2 ( Descriptive Statistics and Probability )

MABS Institution

11th Business Maths Monthly Test - 2 ( Descriptive Statistics and Probability )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Harmonic mean is better than other means if the data are for

Speed or rates
Heights or lengths.
Binary values like 0 and 1.
Ratios or proportions.

The correct relationship among A.M.,G.M.and H.M.is:

A.M.
G.M.≥A.M.≥H.M.
H.M.≥G.M.≥A.M.
A.M.≥G.M.≥H.M.

If median = 45 and its coefficient is 0.25, then the mean deviation about median is

11.25
180
0.0056
45

When an observation in the data is zero, then its geometric mean is

Negative
Positive
Zero
Cannot be calculated

The first quartile is also known as

median.
lower quartile.
mode.
third decile

Harmonic mean is the reciprocal of

Median of the values.
Geometric mean of the values.
Arithmetic mean of the reciprocal of the values.
Quartiles of the values.

The probability of drawing a spade from a pack of card is

1/52
1/13
4/13
1/4

If Q₁ = 30 and Q₃ = 50, the coefficient of quartile deviation is

20
40
10
0.25

The two events A and B are mutually exclusive if

\(P\left( A\cap B \right) =0\)
\(P\left( A\cap B \right) =1\)
\(P\left( A\cup B \right) =0\)
\(P\left( AUB \right) =1\)

Let a sample space of an experiment be S = { E₁,E₂,....., En} Then \(\sum _{ i=1 }^{ n }{ P({ E }_{ t }) } \) is equal to

0
1
\(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ 3 } \)

Part - B

Generic 2 - Answer All Question

A person purchases tomatoes from each of the 4 places at the rate of 1kg., 2kg., 3kg., and 4kg. per rupee respectively .On the average, how many kilograms has he purchased per rupee?

An investor buys Rs. 1,500 worth of shares in a company each month. During the first four months he bought the shares at a price of Rs. 10, 15, 20 and 30 per share. What is the average price paid for the shares bought during these four months? Verify your result.

A family has two children. What is the probability that both the children are girls given that at least one of them is a girl?

Find the first quartile and third quartile for the given observations
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

A die is thrown twice and the sum of the number appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

From a pack of 52 cards, two cards are drawn at random. Find the probability that one is a king and the other is a queen.

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have
(i) No woman (ii) One man (iii) No man

Part - C

Generic 3 - Answer All Question

Find the geometric mean for the following data

Value 10 12 15 20 50

Frequency 2 3 10 8 2

Calculate the value of Q₁, Q₃, D₆ and P₅₀ from the following data

Roll No 1 2 3 4 5 6 7

Marks 20 28 40 12 30 15 50

Calculate the harmonic mean for the following data:

Size of items 50-60 60-70 70-80 80-90 90-100

No.of items 12 15 22 18 10

Calculate Quartile deviation and Coefficient of Quartile deviation of the following data.

Marks: 0 10 20 30 40 50 60 70

No. of
students: 150 142 130 120 72 30 12 4

A card from pack 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be hearts. Find the probability of the missing card to be a heart?

Calculate the Harmonic Mean of the following values:
1, 0.5, 10, 45.0, 175.0, 0.01, 4.0, 11.2

Calculate the harmonic mean for:

Size 6 7 8 9 10 11

Frequency 4 6 9 5 2 8

Part - D

Generic 5 - Answer All Question

Two dice are thrown together. Let A be the event "getting 6 on the first die" and B be the event "getting 2 on the second die". Are the events A and B independent?

Compute the mean deviation about mean from the following data:

Class Interval 0-5 5-10 10-15 15-20 20-25

Frequency f 3 5 12 6 4

Three boxes B₁, B₂, B₃ contain lamp bulbs some of which are defective. The defective proportions in box B₁, box B₂ and box B₃ are respectively \(\frac { 1 }{ 2 } ,\frac { 1 }{ 8 } and\frac { 3 }{ 4 } \)A box is selected at random and a bulb drawn from it. If the selected bulb is found to be defective, what is the probability that box B1 was selected?

A, B and C was 50% , 30% and 20% of the cars in a service station respectively. They fail to clean the glass in 5% , 7% and 3% of the cars respectively. The glass of a washed car is checked. What is the probability that the glass has been cleaned?
Calculate the Mean deviation about median and its relative measure for the following data.

X 15 25 35 45 55 65 75 85

frequency 12 11 10 15 22 13 18 19

The monthly incomes of 8 families in rupees in a certain locality are given below. Calculate the mean, the geometric mean and the harmonic mean and confirm that the relations among them holds true. Verify their relationships among averages.

Family: A B C D E F G H

Income (Rs.): 70 10 50 75 8 25 8 42

Three horses A, B, C are in race. A is twice as likely to win as B and B is twice as likely to win as C. What are their respective probabilities of winning?

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