Tamilnadu State Board New Syllabus Samcheer Kalvi 11th Business Maths Guide Pdf Chapter 8 Descriptive Statistics and Probability Ex 8.3 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 11th Business Maths Solutions Chapter 8 Descriptive Statistics and Probability Ex 8.3

### Samacheer Kalvi 11th Business Maths Descriptive Statistics and Probability Ex 8.3 Text Book Back Questions and Answers

Choose the correct answer.

Question 1.

Which of the following is a positional measure?

(a) Range

(b) Mode

(c) Mean deviation

(d) Percentiles

Answer:

(d) Percentiles

Question 2.

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

(a) Weighted mean

(b) Arithmetic mean

(c) Geometric mean

(d) Harmonic mean

Answer:

(c) Geometric mean

Question 3.

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

(a) Negative

(b) Positive

(c) Zero

(d) Cannot be calculated

Answer:

(c) Zero

Question 4.

The best measure of central tendency is:

(a) Arithmetic mean

(b) Harmonic mean

(c) Geometric mean

(d) Median

Answer:

(a) Arithmetic mean

Question 5.

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

(a) \(\frac{12}{13}\)

(b) 12

(c) \(\frac{36}{13}\)

(d) \(\frac{13}{36}\)

Answer:

(c) \(\frac{36}{13}\)

Hint:

Here n = 3

Question 6.

The geometric mean of two numbers 8 and 18 shall be:

(a) 12

(b) 13

(c) 15

(d) 11.08

Answer:

(a) 12

Hint:

Question 7.

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

(a) A.M. < G.M. < H.M.

(b) G.M. > A.M. > H.M.

(c) H.M. > G.M. > A.M.

(d) A.M. > G.M. > H.M.

Answer:

(d) A.M. > G.M. > H.M.

Question 8.

Harmonic mean is the reciprocal of:

(a) Median of the values.

(b) Geometric mean of the values.

(c) Arithmetic mean of the reciprocal of the values.

(d) Quartiles of the values.

Answer:

(c) Arithmetic mean of the reciprocal of the values.

Question 9.

Median is same as:

(a) Q_{1}

(b) Q_{2}

(c) Q_{3}

(d) D_{2}

Answer:

(b) Q_{2}

Question 10.

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

(a) 10

(b) 12

(c) 14

(d) 9

Answer:

(a) 10

Hint:

The ascending order of 10, 14, 11, 9, 8, 12, 6 is 6, 8, 9, 10, 11, 12, 14.

In this order middle number is 10.

Median = \(\left(\frac{n+1}{2}\right)^{t h}\) value

= \(\left(\frac{7+1}{2}\right)^{th}\)

= 10

∴ Median 10.

Question 11.

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

(a) 15

(b) 11

(c) 12.5

(d) 13

Answer:

(d) 13

Hint: The values are in ascending, order.

∴ The mean is the middle value.

Question 12.

If the mean of 1, 2, 3, ….., n is \(\frac{6 n}{11}\), then the value of n is:

(a) 10

(b) 12

(c) 11

(d) 13

Answer:

(c) 11

Hint:

The mean of 1, 2, 3,…., n is \(\frac{6 n}{11}\)

i.e., \(\frac{1+2+3+4 \ldots+n}{n}=\frac{6 n}{11}\)

\(\frac{\frac{n(n+1)}{2}}{n}=\frac{6 n}{11}\)

\(\frac{n+1}{2}=\frac{6 n}{11}\)

11(n + 1) = 2 × 6

11n + 11 = 12n

∴ n = 11

Question 13.

The harmonic mean is better than other means if the data are for:

(a) Speed or rates.

(b) Heights or lengths.

(c) Binary values like 0 and 1.

(d) Ratios or proportions.

Answer:

(a) Speed or rates

Question 14.

The first quartile is also known as:

(a) median

(b) lower quartile

(c) mode

(d) third decile

Answer:

(b) lower quartile

Question 15.

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

(a) 20

(b) 40

(c) 10

(d) 0.25

Answer:

(d) 0.25

Hint:

Coefficient of quartile deviation is = \(\frac{Q_{3}-Q_{1}}{Q_{3}+Q_{1}}\)

= \(\frac{50-30}{50+30}\)

= \(\frac{20}{40}\)

= 0.25

Question 16.

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

(a) 11.25

(b) 180

(c) 0.0056

(d) 45

Answer:

(a) 11.25

Hint:

Coefficient of M.D = \(\frac{\mathrm{MD}}{\mathrm{Median}}\)

MD = Coefficient of MD × Median

= 0.25 × 45

= 11.25

Question 17.

The two events A and B are mutually exclusive if:

(a) P(A ∩ B) = 0

(b) P(A ∩ B) = 1

(c) P(A ∪ B) = 0

(d) P(A ∪ B) = 1

Answer:

(a) P(A ∩ B) = 0

Question 18.

The events A and B are independent if:

(a) P(A ∩ B) = 0

(b) P(A ∩ B) = P(A) × P(B)

(c) P(A ∩ B) = P(A) + P(B)

(d) P(A ∪ B) = P(A) × P(B)

Answer:

(b) P(A ∩ B) = P(A) × P(B)

Question 19.

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

(a) P(A) P(B/A)

(b) \(\frac{P(A \cap B)}{P(B)}\)

(c) \(\frac{P(A \cap B)}{P(A)}\)

(d) P(A) P(A/B)

Answer:

(c) \(\frac{P(A \cap B)}{P(A)}\)

Question 20.

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

(a) \(\frac{1}{52}\)

(b) \(\frac{1}{13}\)

(c) \(\frac{4}{13}\)

(d) \(\frac{1}{4}\)

Answer:

(d) \(\frac{1}{4}\)

Hint:

Number of spade cards is 13.

Total number of cards in pack = 52

Probability of drawing a spade card is = \(\frac{13}{52}=\frac{1}{4}\)

Question 21.

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

(a) Mutually exclusive

(b) Dependent

(c) Not disjoint

(d) Independent

Answer:

(d) Independent

Question 22.

Let a sample space of an experiment be S = {E_{1}, E_{2}, …., E_{n}} then \(\sum_{i=1}^{n} \mathrm{P}\left(\mathrm{E}_{i}\right)\) is equal to:

(a) 0

(b) 1

(c) \(\frac{1}{2}\)

(d) \(\frac{1}{3}\)

Answer:

(b) 1

Hint:

Sum of probabilities is 1

i.e., \(\sum_{i=1}^{n} \mathrm{P}\left(\mathrm{E}_{i}\right)=1\)

Question 23.

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

(a) \(\frac{1}{36}\)

(b) 0

(c) \(\frac{1}{3}\)

(d) \(\frac{1}{6}\)

Answer:

(a) \(\frac{1}{36}\)

Hint:

When a pair of dice is rolled number of elements in the sample space is 36.

2 is the only even prime number. (2, 2) is the only event of even prime number on both dice.

Required probabilities \(\frac{1}{36}\).

Question 24.

Probability of an impossible event is:

(a) 1

(b) 0

(c) 0.2

(d) 0.5

Answer:

(b) 0

Question 25.

The probability that at least one of the events A, B occur is:

(a) P(A ∪ B)

(b) P(A ∩ B)

(c) P(A/B)

(d) (A ∪ B)

Answer:

(a) P(A ∪ B)