#### Chapters

Chapter 2: Algebra

Chapter 3: Analytical Geometry

Chapter 4: Trigonometry

Chapter 5: Differential Calculus

Chapter 6: Applications of Differentiation

Chapter 7: Financial Mathematics

Chapter 8: Descriptive Statistics and Probability

Chapter 9: Correlation and Regression Analysis

Chapter 10: Operations Research

## Chapter 8: Descriptive Statistics and Probability

### 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]

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

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

**Find Q _{1}, Q_{3}, D_{8} and P_{67} 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 |

**Find lower quartile, upper quartile, 7 ^{th} decile, 5^{th} decile and 60^{th} 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 |

**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 |

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?

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?

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?

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 |

**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 |

**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 |

**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 |

**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 |

**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 |

**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 |

**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 |

### 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]

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?

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?

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.

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

- solved
- exactly one of them solves the problem

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?

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

- both balls are red
- both balls are of the same colour.

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.

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

- the first urn
- the second urn
- the third urn

Three boxes B_{1}, B_{2}, B_{3} contain lamp bulbs some of which are defective. The defective proportions in box B_{1}, box B_{2} and box B_{3} 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 B_{1} was selected?

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?

A die is thrown. Find the probability of getting

- a prime number
- a number greater than or equal to 3

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?

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?

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 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

- two aces
- two spades

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?

### 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:

Which of the following is positional measure?

Range

Mode

Mean deviation

Percentiles

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

Weighted mean

Arithmetic mean

Geometric mean

Harmonic mean

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

Negative

Positive

Zero

Cannot be calculated

The best measure of central tendency is _________.

Arithmetic mean

Harmonic mean

Geometric mean

Median

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

`12/13`

12

`36/13`

`13/36`

The geometric mean of two numbers 8 and 18 shall be

12

13

15

11.08

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

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.

Median is the same as:

Q

_{1}Q

_{2}Q

_{3}D

_{2}

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

10

12

14

9

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

15

11

12.5

13

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

10

12

11

13

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 first quartile is also known as _________.

median

lower quartile

mode

third decile

If Q_{1} = 30 and Q_{3} = 50, the coefficient of quartile deviation is

20

40

10

0.25

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

11.25

180

0.0056

45

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

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)

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")`

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

`1/52`

`1/13`

`4/13`

`1/4`

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

Mutually exclusive

Dependent

Not disjoint

Independent

Let a sample space of an experiment be S = {E_{1}, E_{2}, ..., E_{n}}, then `sum_("i" = 1)^"n" "P"("E"_"i")` is equal to

0

1

`1/2`

`1/3`

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`

Probability of an impossible event is _________.

1

0

0.2

0.5

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

P(A ∪ B)

P(A ∩ B)

P`("A"/"B")`

(A ∪ B)

### 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]

**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 |

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.

**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 |

**Calculate Mean deviation about Mean of the following data.**

X |
2 | 5 | 6 | 8 | 10 | 12 |

f |
2 | 8 | 10 | 7 | 8 | 5 |

**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 |

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?

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

- No woman
- One man
- No man

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?

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?

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

## 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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Concepts covered in Class 11th Business Mathematics and Statistics Answers Guide chapter 8 Descriptive Statistics and Probability are Measures of Central Tendency, Measures of Dispersion, Probability.

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