Statistics and Probability One Mark Online Test

Statistics and Probability One Mark Online Test (10th Standard Mathematics)

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Which of the following is not a measure of dispersion?

A.Range B.Standard deviation C.Arithmetic mean D.Variance

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

A.0 B.1 C.8 D.3

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

A.always positive B.always negative C.zero D.a non-zero integer

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

A.40000 B.160900 C.160000 D.30000

Variance of first 20 natural numbers is

A.32.25 B.44.25 C.33.25 D.30

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.225

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.3p C.p + 5 D.9p + 15

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

A.3.5 B.3 C.4.5 D.2.5

Which of the following is incorrect?

A.\(P(A) > 1\) B.\(0 \le P(A) \le 1\) C.\(P(\emptyset) = 0\) D.\(P(A) + P(\overline{A}) = 1\)

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.\(\frac{p}{p + q + r}\) C.\(\frac{p + q}{p + q + r}\) D.\(\frac{p + r}{p + q + r}\)

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.\(\frac{7}{10}\) C.\(\frac{3}{9}\) D.\(\frac{7}{9}\)

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.1 C.3 D.1.5

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.15 D.20

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

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

Q16

If the largest value in a data set is \(85\) and its range is \(38\), what is the smallest value in the data set?

A.\(47\) B.\(123\) C.\(38\) D.\(57\)

Q17

If the standard deviation of a set of observations is \(4.2\) and each observation is increased by \(3.5\), what is the standard deviation of the new set of observations?

A.\(7.7\) B.\(4.2\) C.\(1.2\) D.\(14.7\)

Q18

If the variance of a set of observations is \(9\), and each observation is multiplied by \(3\), what is the standard deviation of the new set of observations?

A.\(9\) B.\(27\) C.\(81\) D.\(3\)

Q19

Find the coefficient of variation of a data set if its mean is \(20\) and its standard deviation is \(5\).

A.\(25\%\) B.\(400\%\) C.\(15\%\) D.\(4\%\)

Q20

Two groups A and B have coefficients of variation \(12.5\%\) and \(18.2\%\) respectively. Which of the following statements is true regarding their consistency?

A.Group B is more consistent than Group A B.Group A is more consistent than Group B C.Both groups are equally consistent D.Consistency cannot be compared using coefficient of variation

Q21

What is the sum of the probability of a sure event and the probability of an impossible event?

A.\(0\) B.\(0.5\) C.\(1\) D.\(2\)

Q22

If the probability of occurrence of an event \(E\) is \(0.35\), what is the probability of the complement event \(\overline{E}\)?

A.\(0.35\) B.\(0.65\) C.\(1.35\) D.\(-0.35\)

Q23

Three unbiased coins are tossed simultaneously. What is the probability of getting at least two heads?

A.\(\frac{1}{2}\) B.\(\frac{3}{8}\) C.\(\frac{7}{8}\) D.\(\frac{1}{4}\)

Q24

For any two events \(A\) and \(B\), if \(P(A) = 0.5\), \(P(B) = 0.4\), and \(P(A \cup B) = 0.7\), what is \(P(A \cap B)\)?

A.\(0.2\) B.\(0.9\) C.\(0.1\) D.\(0.3\)

Q25

If \(A\) and \(B\) are two mutually exclusive events such that \(P(A) = 0.3\) and \(P(B) = 0.4\), what is \(P(A \cup B)\)?

A.\(0.7\) B.\(0.12\) C.\(0.1\) D.\(0.5\)

Q26

What is the variance of the first \(5\) natural numbers?

A.\(2\) B.\(3\) C.\(2.5\) D.\(1.5\)

Q27

When two fair dice are rolled together, what is the total number of sample points in the sample space?

A.\(12\) B.\(36\) C.\(6\) D.\(18\)

Q28

What is the probability that a non-leap year selected at random will contain \(53\) Sundays?

A.\(\frac{2}{7}\) B.\(\frac{1}{7}\) C.\(\frac{53}{365}\) D.\(\frac{1}{365}\)

Q29

Two dice are rolled simultaneously. What is the probability of getting a doublet (equal numbers on both dice)?

A.\(\frac{1}{36}\) B.\(\frac{1}{6}\) C.\(\frac{1}{2}\) D.\(\frac{5}{6}\)

Q30

What is the range of the first \(5\) prime numbers?

A.\(9\) B.\(11\) C.\(7\) D.\(8\)

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About this Statistics and Probability test

This free online practice test covers Statistics and Probability from the 10th Standard Mathematics (Samacheer Kalvi) syllabus. Choose the number of questions and an optional time limit, then answer and submit — everything is checked in your browser, with the correct answers and a worked explanation shown at the end. For the full solutions to every question in this set, see the solved MCQs page.

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