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## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 8 Statistics and Probability Ex 8.5

Multiple Choice Questions

Question 1.

Which of the following is not a measure of dispersion?

(1) Range

(2) Standard deviation

(3) Arithmetic mean

(4) Variance

Solution:

(3) Arithmetic mean

Question 2.

The range of the data 8, 8, 8, 8, 8. . . 8 is _____

(1) 0

(2) 1

(3) 8

(4) 3

Answer:

(1) 0

Hint:

Range = L – S = 8 – 8 = 0

Question 3.

The sum of all deviations of the data from its mean is

(1) Always positive

(2) always negative

(3) zero

(4) non-zero integer

Solution:

(3) zero

Question 4.

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all deviations is ______

(1) 40000

(2) 160900

(3) 160000

(4) 30000

Answer:

(2) 160900

Hint:

Question 5.

Variance of the first 20 natural numbers is

(1) 32.25

(2) 44.25

(3) 33.25

(4) 30

Solution:

(3) 33.25

Question 6.

The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is ______

(1) 3

(2) 15

(3) 5

(4) 225

Answer:

(4) 225

Hint:

Standard deviation = 3

Each value is multiplied by 5

New standard deviation = 3 × 5 = 15

New variance = 152 = 225

Question 7.

If the standard deviation of x, y, z is p then the standard deviation of 3x + 5, 3y + 5, 3z + 5 is

(1) 3p + 5

(2) 3p

(3) p + 5

(4) 9p + 15

Solution:

(2) 3p

Question 8.

If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is _____

(1) 3.5

(2) 3

(3) 4.5

(4) 2.5

Answer:

(1) 3.5

Hint:

Question 9.

Which of the following is incorrect?

(1) P (A) > 1

(2) 0 ≤ P(A) ≤ 1

(3) P(ϕ) = 0 (4)

(4) P (A) + P(\(\overline{\mathbf{A}}\)) = 1

Solution:

(1) P(A) > 1

Question 10.

The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

Solution:

(2) \(\frac{p}{p+q+r}\)

Question 11.

A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

Solution:

(2) \(\frac{7}{10}\)

Question 12.

The probability of getting a job for a person is \(\frac{x}{3}\). If the probability of not getting the job is \(\frac{2}{3}\) then the value of x is ____

(1) 2

(2) 1

(3) 3

(4) 1.5

Answer:

(2) 1

Hint:

Question 13.

Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac{1}{9}\), then the number of tickets bought by Kamalam is

(1) 5

(2) 10

(3) 15

(4) 20

Solution:

(3) 15

Hint:

\(=\frac{1}{9} \times 135=15\)

Question 14.

If a letter is chosen at random from the English alphabets {a, b, ……, z} then the probability that the letter chosen precedes x _______

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

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

(3) \(\frac{23}{26}\)

(4) \(\frac{3}{26}\)

Answer:

(3) \(\frac{23}{26}\)

Hint:

Question 15.

A purse contains 10 notes of ₹ 2000, 15 notes of ₹ 500, and 25 notes of ₹ 200. One note is drawn at random. What is the probability that the note is either a ₹ 500 note or ₹ 200 note?

(1) \(\frac{1}{5}\)

(2) \(\frac{3}{10}\)

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

(4) \(\frac{4}{5}\)

Solution:

(4) \(\frac{4}{5}\)