Tamil Nadu Board of Secondary EducationHSC Commerce Class 11th

# Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 8 - Descriptive Statistics and Probability [Latest edition]

## Chapter 8: Descriptive Statistics and Probability

Exercise 8.1Exercise 8.2Exercise 8.3Miscellaneous Problems
Exercise 8.1 [Pages 194 - 195]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 8 Descriptive Statistics and ProbabilityExercise 8.1 [Pages 194 - 195]

Exercise 8.1 | Q 1 | Page 194

Find the first quartile and third quartile for the given observations.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22

Exercise 8.1 | Q 2 | Page 194

Find Q1, Q3, D8 and P67 of the following data:

 Size of Shares 4 4.5 5 5.5 6 6.5 7 7.5 8 Frequency 10 18 22 25 40 15 10 8 7
Exercise 8.1 | Q 3 | Page 194

Find lower quartile, upper quartile, 7th decile, 5th decile and 60th percentile for the following frequency distribution.

 Wages 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 1 3 11 21 43 32 9
Exercise 8.1 | Q 4 | Page 194

Calculate GM for the following table gives the weight of 31 persons in the sample survey.

 Weight (lbs): 130 135 140 145 146 148 149 150 157 Frequency 3 4 6 6 3 5 2 1 1
Exercise 8.1 | Q 5 | Page 195

The price of a commodity increased by 5% from 2004 to 2005, 8% from 2005 to 2006 and 77% from 2006 to 2007. Calculate the average increase from 2004 to 2007?

Exercise 8.1 | Q 6 | Page 195

An aeroplane flies, along the four sides of a square at speeds of 100, 200, 300 and 400 kilometres per hour respectively. What is the average speed of the plane in its flight around the square?

Exercise 8.1 | Q 7 | Page 195

A man travelled by car for 3 days. He covered 480 km each day. On the first day, he drove for 10 hours at 48 km an hour. On the second day, he drove for 12 hours at 40 km an hour and for the last day he drove for 15 hours at 32 km. What is his average speed?

Exercise 8.1 | Q 8 | Page 195

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
Exercise 8.1 | Q 9 | Page 195

Calculate AM, GM and HM and also verify their relations among them for the following data.

 X 5 15 10 30 25 20 35 40 f 18 16 20 21 22 13 12 16
Exercise 8.1 | Q 10 | Page 195

Calculate AM, GM and HM from the following data and also find its relationship:

 Marks: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 No. of students: 5 10 25 30 20 10
Exercise 8.1 | Q 11 | Page 195

Calculate the quartile deviation and its coefficient from the following data:

 Age in Years: 20 30 40 50 60 70 80 No. of Members: 13 61 47 15 10 18 36
Exercise 8.1 | Q 12 | Page 195

Calculate quartile deviation and its relative measure from the following data:

 X 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 f 5 10 13 18 14 8
Exercise 8.1 | Q 13 | Page 195

Compute mean deviation about median from the following data:

 Height in inches No. of students 58 15 59 20 60 32 61 35 62 35 63 22 64 20 65 10 66 8
Exercise 8.1 | Q 14 | Page 195

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
Exercise 8.1 | Q 15 | Page 195

Find out the coefficient of mean deviation about median in the following series.

 Age in years 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 No. of persons 8 12 16 20 37 25 19 13
Exercise 8.2 [Pages 202 - 204]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 8 Descriptive Statistics and ProbabilityExercise 8.2 [Pages 202 - 204]

Exercise 8.2 | Q 1 | Page 202

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?

Exercise 8.2 | Q 2 | Page 203

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?

Exercise 8.2 | Q 3 | Page 203

An unbiased die is thrown twice. Let the event A be the odd number on the first throw and B the event odd number on the second throw. Check whether A and B events are independent.

Exercise 8.2 | Q 4 | Page 203

Probability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem independently, find the probability that the problem is

1. solved
2. exactly one of them solves the problem
Exercise 8.2 | Q 5 | Page 203

Suppose one person is selected at random from a group of 100 persons are given in the following

 Title Psychologist Socialist Democrat Total Men 15 25 10 50 Women 20 15 15 50 Total 35 40 25 100

What is the probability that the man selected is a Psychologist?

Exercise 8.2 | Q 6 | Page 203

Two urns contain the set of balls as given in the following table

 Title White Red Black Urn 1 10 6 9 Urn 2 3 7 15

One ball is drawn from each urn and find the probability that

1. both balls are red
2. both balls are of the same colour.
Exercise 8.2 | Q 7 | Page 203

Bag I contains 3 Red and 4 Black balls while another Bag II contains 5 Red and 6 Black balls. One ball is drawn at random from one of the bags and it is found to be red. Find the probability that it was drawn from Bag I.

Exercise 8.2 | Q 8 | Page 203

The first of three urns contains 7 White and 10 Black balls, the second contains 5 White and 12 Black balls and the third contains 17 White balls and no Black ball. A person chooses an urn at random and draws a ball from it. And the ball is found to be White. Find the probabilities that the ball comes from

1. the first urn
2. the second urn
3. the third urn
Exercise 8.2 | Q 9 | Page 203

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 1/2, 1/8 and 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?

Exercise 8.2 | Q 10 | Page 203

Three horses A, B, C are in the 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?

Exercise 8.2 | Q 11 | Page 203

A die is thrown. Find the probability of getting

1. a prime number
2. a number greater than or equal to 3
Exercise 8.2 | Q 12 | Page 203

Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 4. What is the probability that it is an even number?

Exercise 8.2 | Q 13 | Page 204

There are 1000 students in a school out of which 450 are girls. It is known that out of 450, 20% of the girls studying in class XI. A student is randomly selected from 1000 students. What is the probability that the selected student is from class XI given that the selected student is a girl?

Exercise 8.2 | Q 14 | Page 204

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.

Exercise 8.2 | Q 15 | Page 204

A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of drawing

1. two aces
Exercise 8.2 | Q 16 | Page 204

A company has three machines A, B, C which produces 20%, 30% and 50% of the product respectively. Their respective defective percentages are 7, 3 and 5. From these products, one is chosen and inspected. If it is defective what is the probability that it has been made by machine C?

Exercise 8.3 [Pages 204 - 205]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 8 Descriptive Statistics and ProbabilityExercise 8.3 [Pages 204 - 205]

#### Choose the correct answer:

Exercise 8.3 | Q 1 | Page 204

Which of the following is positional measure?

• Range

• Mode

• Mean deviation

• Percentiles

Exercise 8.3 | Q 2 | Page 204

When calculating the average growth of the economy, the correct mean to use is?

• Weighted mean

• Arithmetic mean

• Geometric mean

• Harmonic mean

Exercise 8.3 | Q 3 | Page 204

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

• Negative

• Positive

• Zero

• Cannot be calculated

Exercise 8.3 | Q 4 | Page 204

The best measure of central tendency is _________.

• Arithmetic mean

• Harmonic mean

• Geometric mean

• Median

Exercise 8.3 | Q 5 | Page 204

The harmonic mean of the numbers 2, 3, 4 is:

• 12/13

• 12

• 36/13

• 13/36

Exercise 8.3 | Q 6 | Page 204

The geometric mean of two numbers 8 and 18 shall be

• 12

• 13

• 15

• 11.08

Exercise 8.3 | Q 7 | Page 204

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

• A.M. < G.M. < H.M.

• G.M. ≥ A.M. ≥ H.M.

• H.M. ≥ G.M. ≥ A.M.

• A.M. ≥ G.M. ≥ H.M

Exercise 8.3 | Q 8 | Page 204

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.

Exercise 8.3 | Q 9 | Page 204

Median is the same as:

• Q1

• Q2

• Q3

• D2

Exercise 8.3 | Q 10 | Page 205

The median of 10, 14, 11, 9, 8, 12, 6 is

• 10

• 12

• 14

• 9

Exercise 8.3 | Q 11 | Page 205

The mean of the values 11, 12, 13, 14 and 15 is

• 15

• 11

• 12.5

• 13

Exercise 8.3 | Q 12 | Page 205

If the mean of 1, 2, 3, …, n is (6"n")/11, then the value of n is

• 10

• 12

• 11

• 13

Exercise 8.3 | Q 13 | Page 205

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.

Exercise 8.3 | Q 14 | Page 205

The first quartile is also known as _________.

• median

• lower quartile

• mode

• third decile

Exercise 8.3 | Q 15 | Page 205

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

• 20

• 40

• 10

• 0.25

Exercise 8.3 | Q 16 | Page 205

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

• 11.25

• 180

• 0.0056

• 45

Exercise 8.3 | Q 17 | Page 205

The two events A and B are mutually exclusive if

• P(A ∩ B) = 0

• P(A ∩ B) = 1

• P(A ∪ B) = 0

• P(A ∪ B) = 1

Exercise 8.3 | Q 18 | Page 205

The events A and B are independent if

• P(A ∩ B) = 0

• P(A ∩ B) = P(A) × P(B)

• P(A ∩ B) = P(A) + P(B)

• P(A ∪ B) = P(A) × P(B)

Exercise 8.3 | Q 19 | Page 205

If two events A and B are dependent then the conditional probability of P("B"/"A") is

• "P"("A") "P"("B"/"A")

• ("P"("A" ∩ "B"))/("P"("B"))

• ("P"("A" ∩ "B"))/("P"("A"))

• "P"("A") "P"("A"/"B")

Exercise 8.3 | Q 20 | Page 205

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

• 1/52

• 1/13

• 4/13

• 1/4

Exercise 8.3 | Q 21 | Page 205

If the outcome of one event does not influence another event then the two events are

• Mutually exclusive

• Dependent

• Not disjoint

• Independent

Exercise 8.3 | Q 22 | Page 205

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

• 0

• 1

• 1/2

• 1/3

Exercise 8.3 | Q 23 | Page 205

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

• 1/36

• 0

• 1/3

• 1/6

Exercise 8.3 | Q 24 | Page 205

Probability of an impossible event is _________.

• 1

• 0

• 0.2

• 0.5

Exercise 8.3 | Q 25 | Page 205

Probability that at least one of the events A, B occur is

• P(A ∪ B)

• P(A ∩ B)

• P("A"/"B")

• (A ∪ B)

Miscellaneous Problems [Pages 205 - 206]

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 8 Descriptive Statistics and ProbabilityMiscellaneous Problems [Pages 205 - 206]

Miscellaneous Problems | Q 1 | Page 205

Find out the GM for the following.

 Yield of Rice (tones) No. of farms 7.5 - 10.5 5 10.5 - 13.5 9 13.5 - 16.5 19 16.5 - 19.5 23 19.5 - 22.5 7 22.5 - 25.5 4 25.5 - 28.5 1
Miscellaneous Problems | Q 2 | Page 206

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

Miscellaneous Problems | Q 3 | Page 206

Calculate the Mean deviation about median of the following data.

 Class interval: 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency: 6 7 15 16 4 2
Miscellaneous Problems | Q 4 | Page 206

Calculate Mean deviation about Mean of the following data.

 X 2 5 6 8 10 12 f 2 8 10 7 8 5
Miscellaneous Problems | Q 5 | Page 206

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
Miscellaneous Problems | Q 6 | Page 206

In a screw factory machines A, B, C manufacture respectively 30%, 40% and 30% of the total output of these 2%, 4% and 6% percent are defective screws. A screw is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by Machine C?

Miscellaneous Problems | Q 7 | Page 206

A committee of two persons is formed from 3 men and 2 women. What is the probability that the committee will have

1. No woman
2. One man
3. No man
Miscellaneous Problems | Q 8 | Page 206

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?

Miscellaneous Problems | Q 9 | Page 206

Data on readership of a magazine indicates that the proportion of male readers over 30 years old is 0.30 and the proportion of male readers under 30 is 0.20. If the proportion of readers under 30 is 0.80. What is the probability that a randomly selected male subscriber is under 30?

Miscellaneous Problems | Q 10 | Page 206

Gun 1 and Gun 2 are shooting at the same target. Gun 1 shoots on the average nine shots during the same time Gun 2 shoots 10 shots. The precision of these two guns is not the same. On the average, out of 10 shots from Gun 2 seven hit the target. In the course of shooting the target has been hit by a bullet, but it is not known which Gunshot this bullet. Find the chance that the target was hit by Gun 2?

## Chapter 8: Descriptive Statistics and Probability

Exercise 8.1Exercise 8.2Exercise 8.3Miscellaneous Problems

## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 8 - Descriptive Statistics and Probability

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