Chapter 13 · Statistics and Probability

NCERT Exemplar Class 10 Maths Exercise 13.1

All 26 questions of NCERT Exemplar Class 10 Maths Exercise 13.1 (Statistics and Probability), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   In the formula $\bar{x}=a+\frac{\sum f_i{d}_i}{\sum f_i}$, ​for finding ​the ​mean ​of grouped ​data $d_i$'s are ​deviations from $a$ of

   1. (a)lower limits of the classes
   2. (b)upper limits of the classes
   3. (c)mid points of the classes
   4. (d)frequencies of the class marks
   Show answer

   (c) mid points of the classes

   Step-by-step solution →
2. Q2
   While computing mean ​of grouped ​data, ​we assume ​that the frequencies ​are

   1. (a)evenly distributed over all the classes
   2. (b)centred at the classmarks of the classes
   3. (c)centred at the upper limits of the classes
   4. (d)centred at the lower limits of the classes
   Show answer

   (b) centred at the classmarks of the classes

   Step-by-step solution →
3. Q3
   If $x_i$'s are the mid points of ​the ​class intervals of grouped data, $f_i$'s are ​the ​corresponding frequencies ​and $\bar{x}$ is the mean, ​then $\sum (f_i{x}_i-\bar{x})$ ​is equal to

   1. (a)$0$
   2. (b)$-1$
   3. (c)$1$
   4. (d)$2$
   Show answer

   (a) $0$

   Step-by-step solution →
4. Q4
   In ​the ​formula $\bar{x}=a+h\frac{\sum f_i{u}_i}{\sum f_i}$, ​for finding ​the mean ​of ​grouped frequency distribution, $u_i=$

   1. (a)$\frac{x_i+a}{h}$
   2. (b)$h(x_i-a)$
   3. (c)$\frac{x_i-a}{h}$
   4. (d)$\frac{a-x_i}{h}$
   Show answer

   (c) $\frac{x_i-a}{h}$

   Step-by-step solution →
5. Q5
   The abscissa of ​the point of intersection of ​the less ​than type and ​of the more than type cumulative frequency curves of a ​grouped data ​gives ​its

   1. (a)mean
   2. (b)median
   3. (c)mode
   4. (d)all the three above
   Show answer

   (b) median

   Step-by-step solution →
6. Q6
   For ​the following distribution, the sum of ​lower ​limits ​of ​the median class ​and modal ​class is

   Class-frequency distribution

   Class	Frequency
   0 - 5	10
   5 - 10	15
   10 - 15	12
   15 - 20	20
   20 - 25	9

   1. (a)$15$
   2. (b)$25$
   3. (c)$30$
   4. (d)$35$
   Show answer

   (b) $25$

   Step-by-step solution →
7. Q7
   Consider the following ​frequency distribution. ​The upper ​limit of the median ​class is

   Frequency distribution

   Class	Frequency
   0 - 5	13
   6 - 11	10
   12 - 17	15
   18 - 23	8
   24 - 29	11

   1. (a)17
   2. (b)17.5
   3. (c)18
   4. (d)18.5
   Show answer

   (b) 17.5

   Step-by-step solution →
8. Q8
   For the ​following ​distribution, the ​modal ​class ​is

   Cumulative marks distribution

   Marks	Number of students
   Below 10	3
   Below 20	12
   Below 30	27
   Below 40	57
   Below 50	75
   Below 60	80

   1. (a)$10$-$20$
   2. (b)$20$-$30$
   3. (c)$30$-$40$
   4. (d)$50$-$60$
   Show answer

   (c) $30$-$40$

   Step-by-step solution →
9. Q9
   Consider ​the following frequency ​distribution. The difference of the ​upper limit ​of the ​median class and the lower limit ​of the modal ​class ​is

   Class-frequency distribution

   Class	Frequency
   65 - 85	4
   85 - 105	5
   105 - 125	13
   125 - 145	20
   145 - 165	14
   165 - 185	7
   185 - 205	4

   1. (a)$0$
   2. (b)$19$
   3. (c)$20$
   4. (d)$38$
   Show answer

   (c) $20$

   Step-by-step solution →
10. Q10
    The times, in seconds, taken ​by $150$ athletes to run a $110$ m hurdle race are ​tabulated below. The number of athletes who ​completed the race in less than ​14.6 ​seconds ​is

    Times of 150 athletes in a 110 m hurdle race

    Class (seconds)	Frequency
    13.8 - 14	2
    14 - 14.2	4
    14.2 - 14.4	5
    14.4 - 14.6	71
    14.6 - 14.8	48
    14.8 - 15	20

    1. (a)$11$
    2. (b)$71$
    3. (c)$82$
    4. (d)$130$
    Show answer

    (c) $82$

    Step-by-step solution →
11. Q11
    Consider ​the ​following ​distribution: ​the frequency ​of the class 30-40 ​is

    Cumulative ('more than') distribution

    Marks obtained	Number of students
    More than or equal to 0	63
    More than or equal to 10	58
    More than or equal to 20	55
    More than or equal to 30	51
    More than or equal to 40	48
    More than or equal to 50	42

    1. (a)3
    2. (b)4
    3. (c)48
    4. (d)51
    Show answer

    (a) 3

    Step-by-step solution →
12. Q12
    If an ​event cannot ​occur, ​then its ​probability is

    1. (a)1
    2. (b)$\frac{3}{4}$
    3. (c)$\frac{1}{2}$
    4. (d)0
    Show answer

    (d) 0

    Step-by-step solution →
13. Q13
    Which of ​the following cannot ​be the ​probability ​of ​an ​event?

    1. (a)$\frac{1}{3}$
    2. (b)$0.1$
    3. (c)$3\%$
    4. (d)$\frac{17}{16}$
    Show answer

    (d) $\frac{17}{16}$

    Step-by-step solution →
14. Q14
    An ​event ​is very unlikely to happen. ​Its probability ​is ​closest ​to

    1. (a)0.0001
    2. (b)0.001
    3. (c)0.01
    4. (d)0.1
    Show answer

    (a) 0.0001

    Step-by-step solution →
15. Q15
    If the probability ​of ​an ​event ​is $p$, ​the probability ​of its ​complementary event will be

    1. (a)$p-1$
    2. (b)$p$
    3. (c)$1-p$
    4. (d)$1-\frac{1}{p}$
    Show answer

    (c) $1-p$

    Step-by-step solution →
16. Q16
    The probability expressed as a percentage of ​a ​particular occurrence ​can ​never ​be

    1. (a)less than 100
    2. (b)less than 0
    3. (c)greater than 1
    4. (d)anything but a whole number
    Show answer

    (b) less than 0

    Step-by-step solution →
17. Q17
    If $P(A)$ denotes ​the ​probability ​of an ​event $A$, then

    1. (a)$P(A)<0$
    2. (b)$P(A)>1$
    3. (c)$0\le P(A)\le 1$
    4. (d)$-1\le P(A)\le 1$
    Show answer

    (c) $0\le P(A)\le 1$

    Step-by-step solution →
18. Q18
    A card is ​selected from ​a deck of ​52 ​cards. ​The probability of ​its being a ​red face card ​is

    1. (a)$\frac{3}{26}$
    2. (b)$\frac{3}{13}$
    3. (c)$\frac{2}{13}$
    4. (d)$\frac{1}{2}$
    Show answer

    (a) $\frac{3}{26}$

    Step-by-step solution →
19. Q19
    The probability ​that a ​non leap year ​selected at ​random will contain ​53 Sundays is

    1. (a)$\frac{1}{7}$
    2. (b)$\frac{2}{7}$
    3. (c)$\frac{3}{7}$
    4. (d)$\frac{5}{7}$
    Show answer

    (a) $\frac{1}{7}$

    Step-by-step solution →
20. Q20
    When ​a die is ​thrown, ​the probability of ​getting ​an ​odd number ​less than $3$ is

    1. (a)$\frac{1}{6}$
    2. (b)$\frac{1}{3}$
    3. (c)$\frac{1}{2}$
    4. (d)$0$
    Show answer

    (a) $\frac{1}{6}$

    Step-by-step solution →
21. Q21
    A card is drawn ​from a ​deck of 52 ​cards. The event ​E is that card is ​not ​an ​ace of hearts. The number of outcomes favourable to E ​is

    1. (a)$4$
    2. (b)$13$
    3. (c)$48$
    4. (d)$51$
    Show answer

    (d) $51$

    Step-by-step solution →
22. Q22
    The probability of ​getting a bad ​egg ​in a lot of 400 is ​0.035. The number of bad eggs ​in the ​lot is

    1. (a)$7$
    2. (b)$14$
    3. (c)$21$
    4. (d)$28$
    Show answer

    (b) $14$

    Step-by-step solution →
23. Q23
    A girl calculates that the probability of her winning the ​first prize in ​a ​lottery is $0.08$. If $6000$ ​tickets ​are sold, how many tickets has ​she bought?

    1. (a)$40$
    2. (b)$240$
    3. (c)$480$
    4. (d)$750$
    Show answer

    (c) $480$

    Step-by-step solution →
24. Q24
    One ticket is drawn at random from ​a ​bag containing tickets ​numbered 1 to 40. ​The probability that ​the selected ticket has a ​number which is a multiple ​of 5 is

    1. (a)$\frac{1}{5}$
    2. (b)$\frac{3}{5}$
    3. (c)$\frac{4}{5}$
    4. (d)$\frac{1}{3}$
    Show answer

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

    Step-by-step solution →
25. Q25
    Someone is ​asked to ​take a ​number ​from ​1 to 100. The probability that it is a ​prime ​is

    1. (a)$\frac{1}{5}$
    2. (b)$\frac{6}{25}$
    3. (c)$\frac{1}{4}$
    4. (d)$\frac{13}{50}$
    Show answer

    (c) $\frac{1}{4}$

    Step-by-step solution →
26. Q26
    A ​school has five houses A, B, C, D and E. ​A class has ​23 students, 4 from house A, 8 ​from house B, 5 from house C, 2 from house D and rest from ​house E. A single student is ​selected at random to be the class monitor. The ​probability that the selected student is not ​from A, B and C is

    1. (a)$\frac{4}{23}$
    2. (b)$\frac{6}{23}$
    3. (c)$\frac{8}{23}$
    4. (d)$\frac{17}{23}$
    Show answer

    (b) $\frac{6}{23}$

    Step-by-step solution →