Every Book Back multiple-choice question from Statistics and Probability (10th Standard Mathematics, Samacheer Kalvi) — each with the correct option highlighted and a clear, worked explanation. Free to read in English and Tamil.
Q1
Which of the following is not a measure of dispersion?
- A. Range
- B. Standard deviation
- C. Arithmetic meanCorrect
- D. Variance
Explanation. Arithmetic mean is a measure of central tendency, whereas range, standard deviation, and variance are measures of dispersion.
Q2
The range of the data 8, 8, 8, 8, 8, ..., 8 is
- A. 0Correct
- B. 1
- C. 8
- D. 3
Explanation. Range is the difference between the largest and smallest values. Since all values in the data set are 8, the difference is 8 - 8 = 0.
Q3
The sum of all deviations of the data from its mean is
- A. always positive
- B. always negative
- C. zeroCorrect
- D. a non-zero integer
Explanation. By the properties of the arithmetic mean, the algebraic sum of the deviations of a set of observations from their mean is always equal to zero.
Q4
The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all observations is
- A. 40000
- B. 160900Correct
- C. 160000
- D. 30000
Explanation. Using the variance formula, the sum of squares is equal to n times the sum of variance and mean squared, which evaluates to 100 times (9 + 1600) = 160900.
Q5
Variance of first 20 natural numbers is
- A. 32.25
- B. 44.25
- C. 33.25Correct
- D. 30
Explanation. The variance of the first n natural numbers is given by (n squared minus 1) divided by 12. Substituting n = 20 gives 399 divided by 12, which is 33.25.
Q6
The standard deviation of a data is 3. If each value is multiplied by 5, then the new variance is
- A. 3
- B. 15
- C. 5
- D. 225Correct
Explanation. When each value is multiplied by 5, the standard deviation is also multiplied by 5, becoming 15. The new variance is 15 squared, which is 225.
Q7
If the standard deviation of x, y, z is p, then the standard deviation of 3x + 5, 3y + 5, 3z + 5 is
- A. 3p + 5
- B. 3pCorrect
- C. p + 5
- D. 9p + 15
Explanation. Standard deviation is unaffected by adding a constant (change of origin) but is multiplied by the scale factor when values are multiplied. Thus, the standard deviation becomes 3p.
Q8
If the mean and coefficient of variation of a data are 4 and 87.5% respectively, then the standard deviation is
- A. 3.5Correct
- B. 3
- C. 4.5
- D. 2.5
Explanation. The coefficient of variation equals standard deviation divided by mean, multiplied by 100. Standard deviation is therefore 87.5 times 4 divided by 100, which equals 3.5.
Q9
Which of the following is incorrect?
- A. \(P(A) > 1\)Correct
- B. \(0 \le P(A) \le 1\)
- C. \(P(\emptyset) = 0\)
- D. \(P(A) + P(\overline{A}) = 1\)
Explanation. The probability of any event always lies within the interval from 0 to 1 inclusive. Thus, the statement that probability of A is greater than 1 is incorrect.
Q10
The probability of selecting a red marble at random from a jar containing p red, q blue, and r green marbles is
- A. \(\frac{q}{p + q + r}\)
- B. \(\frac{p}{p + q + r}\)Correct
- C. \(\frac{p + q}{p + q + r}\)
- D. \(\frac{p + r}{p + q + r}\)
Explanation. The total number of marbles is p + q + r. The number of favorable outcomes for selecting a red marble is p. The probability is p divided by (p + q + r).
Q11
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
- A. \(\frac{3}{10}\)
- B. \(\frac{7}{10}\)Correct
- C. \(\frac{3}{9}\)
- D. \(\frac{7}{9}\)
Explanation. The digit at the units place can be any of the 10 digits from 0 to 9. The favorable digits less than 7 are 0, 1, 2, 3, 4, 5, and 6 (7 digits). The probability is 7/10.
Q12
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
- A. 2
- B. 1Correct
- C. 3
- D. 1.5
Explanation. The sum of probabilities of complementary events is 1. Thus, x/3 plus 2/3 equals 1, which gives x plus 2 equals 3, and solving for x yields 1.
Q13
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
- A. 5
- B. 10
- C. 15Correct
- D. 20
Explanation. The probability of winning is the number of tickets bought divided by the total tickets sold. Setting n/135 equal to 1/9 gives n equal to 135 divided by 9, which is 15.
Q14
If a letter is chosen at random from the English alphabets \(\{a, b, ..., z\}\), then the probability that the letter chosen precedes x is
- A. \(\frac{12}{13}\)
- B. \(\frac{1}{13}\)
- C. \(\frac{23}{26}\)Correct
- D. \(\frac{3}{26}\)
Explanation. There are 26 letters in the English alphabet. The letters preceding x are the 23 letters from a to w. Thus, the probability of selecting such a letter is 23/26.
Q15
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?
- A. \(\frac{1}{5}\)
- B. \(\frac{3}{10}\)
- C. \(\frac{2}{3}\)
- D. \(\frac{4}{5}\)Correct
Explanation. The total number of notes is 10 + 15 + 25 = 50. The number of favorable outcomes (₹500 or ₹200 notes) is 15 + 25 = 40. The probability is 40/50, which reduces to 4/5.
