Exercise 8.3 - Chapter 8 - Descriptive Statistics and Probability - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 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:

Answer:

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) Q₁
(b) Q₂
(c) Q₃
(d) D₂
Answer:
(b) Q₂

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

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 6n/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 6n/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 Q₁ = 30 and Q₃ = 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

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 

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)

Question 20.
The probability of drawing a spade from a pack of card is:

Answer:

Hint:
Number of spade cards is 13.
Total number of cards in pack = 52
Probability of drawing a spade card is 

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 = {E₁, E₂, …., E_n} the  is equal to:

(a) 0
(b) 1

Answer:
(b) 1
Hint:
Sum of probabilities is 1

Question 23.
The probability of obtaining an even prime number on each die, when a pair of dice is rolled is:

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

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)