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NCERT Exemplar · Class 9 Mathematics Statistics and Probability

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EXERCISE 14.1 21–30 (part 3 of 7)

  1. The number of classes in the distribution will be :

    Exercise 21

    The median of the data 78\displaystyle 78, 56\displaystyle 56, 22\displaystyle 22, 34\displaystyle 34, 45\displaystyle 45, 54\displaystyle 54, 39\displaystyle 39, 68\displaystyle 68, 54\displaystyle 54, 84\displaystyle 84 is (A) 45\displaystyle 45 (B) 49.5\displaystyle 49.5 (C) 54\displaystyle 54 (D) 56\displaystyle 56

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    NCERT’s answer
    (C)
    (C) \(\displaystyle 54\). \[22,\,34,\,39,\,45,\,54,\,54,\,56,\,68,\,78,\,84 \] \[\text{Median} = \frac{5^{\text{th}}+6^{\text{th}}\text{ term}}{2} = \frac{54+54}{2} = 54 \]

  2. Exercise 22

    For drawing a frequency polygon of a continous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abcissae are respectively : (A) upper limits of the classes (B) lower limits of the classes (C) class marks of the classes (D) upper limits of perceeding classes

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    NCERT’s answer
    (C)
    (C) class marks of the classes. \[\text{class mark} = \frac{\text{lower limit}+\text{upper limit}}{2} \] A frequency polygon plots each class's frequency against this midpoint, not either raw limit.

  3. Exercise 23

    Median of the following numbers: 4\displaystyle 4, 4\displaystyle 4, 5\displaystyle 5, 7\displaystyle 7, 6\displaystyle 6, 7\displaystyle 7, 7\displaystyle 7, 12\displaystyle 12, 3\displaystyle 3 is (A) 4\displaystyle 4 (B) 5\displaystyle 5 (C) 6\displaystyle 6 (D) 7\displaystyle 7

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    NCERT’s answer
    (C)
    (C) \(\displaystyle 6\). \[3,\,4,\,4,\,5,\,6,\,7,\,7,\,7,\,12 \] \[\text{Median} = \left(\frac{n+1}{2}\right)^{\text{th}}\text{ term} = 5^{\text{th}}\text{ term} = 6 \]

  4. Exercise 24

    Mode of the data 15\displaystyle 15, 14\displaystyle 14, 19\displaystyle 19, 20\displaystyle 20, 14\displaystyle 14, 15\displaystyle 15, 16\displaystyle 16, 14\displaystyle 14, 15\displaystyle 15, 18\displaystyle 18, 14\displaystyle 14, 19\displaystyle 19, 15\displaystyle 15, 17\displaystyle 17, 15\displaystyle 15 is (A) 14\displaystyle 14 (B) 15\displaystyle 15 (C) 16\displaystyle 16 (D) 17\displaystyle 17

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    NCERT’s answer
    (B)
    (B) \(\displaystyle 15\). \[14:4,\quad 15:5,\quad 16:1,\quad 17:1,\quad 18:1,\quad 19:2,\quad 20:1 \] \(\displaystyle 15\) occurs most often, \(\displaystyle 5\) times, so it is the mode.

  5. Exercise 25

    In a sample study of 642\displaystyle 642 people, it was found that 514\displaystyle 514 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is : (A) 0.5\displaystyle 0.5 (B) 0.6\displaystyle 0.6 (C) 0.7\displaystyle 0.7 (D) 0.8\displaystyle 0.8

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    NCERT’s answer
    (D)
    (D) \(\displaystyle 0.8\)Sample of $\displaystyle 642$ people; $\displaystyle 514$ hold a high school certificate. \[P(\text{certificate}) = \frac{514}{642} \] \[P(\text{certificate}) \approx 0.8 \]

  6. Exercise 26

    In a survey of 364\displaystyle 364 children aged 19\displaystyle 19-36\displaystyle 36 months, it was found that 91\displaystyle 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is : (A) 0.25\displaystyle 0.25 (B) 0.50\displaystyle 0.50 (C) 0.75\displaystyle 0.75 (D) 0.80\displaystyle 0.80

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    NCERT’s answer
    (C)
    (C) \(\displaystyle 0.75\)Survey of $\displaystyle 364$ children; $\displaystyle 91$ liked potato chips. \[P(\text{likes chips}) = \frac{91}{364} = 0.25 \] \[P(\text{does not like}) = 1-0.25 = 0.75 \]

  7. Exercise 27

    In a medical examination of students of a class, the following blood groups are recorded:
    Blood groupAABBO
    Number of students10\displaystyle 1013\displaystyle 1312\displaystyle 125\displaystyle 5
    A student is selected at random from the class. The probability that he/she has blood group B, is: (A) 14\displaystyle \frac{1}{4} (B) 1340\displaystyle \frac{13}{40} (C) 310\displaystyle \frac{3}{10} (D) 18\displaystyle \frac{1}{8}

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    NCERT’s answer
    (C)
    (C) \(\displaystyle \frac{3}{10}\) \[\text{Total students} = 10+13+12+5 = 40 \] \[P(\text{blood group B}) = \frac{12}{40} = \frac{3}{10} \]Answer: \(\displaystyle \dfrac{3}{10}\).
  8. A student is selected at random from the class. The probability that he/she has blood group B, is :

    Exercise 28

    Two coins are tossed 1000\displaystyle 1000 times and the outcomes are recorded as below :
    Number of heads2\displaystyle 21\displaystyle 10\displaystyle 0
    Frequency200\displaystyle 200550\displaystyle 550250\displaystyle 250
    Based on this information, the probability for at most one head is (A) 15\displaystyle \frac{1}{5} (B) 14\displaystyle \frac{1}{4} (C) 45\displaystyle \frac{4}{5} (D) 34\displaystyle \frac{3}{4}

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    NCERT’s answer
    (C)
    (C) \(\displaystyle \frac{4}{5}\)At most one head means $\displaystyle 1$ head or $\displaystyle 0$ heads. \[P(\text{at most one head}) = \frac{f(1)+f(0)}{1000} = \frac{550+250}{1000} = \frac{800}{1000} = \frac{4}{5} \]

  9. Exercise 29

    80\displaystyle 80 bulbs are selected at random from a lot and their life time (in hrs) is recorded in the form of a frequency table given below :
    Life time (in hours)300\displaystyle 300500\displaystyle 500700\displaystyle 700900\displaystyle 9001100\displaystyle 1100
    Frequency10\displaystyle 1012\displaystyle 1223\displaystyle 2325\displaystyle 2510\displaystyle 10
    One bulb is selected at random from the lot. The probability that its life is 1150\displaystyle 1150 hours, is (A) 180\displaystyle \frac{1}{80} (B) 716\displaystyle \frac{7}{16} (C) 0\displaystyle 0 (D) 1\displaystyle 1

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    NCERT’s answer
    (C)
    (C) \(\displaystyle 0\)The $\displaystyle 80$ bulbs' lifetimes recorded are only $\displaystyle 300$, $\displaystyle 500$, $\displaystyle 700$, $\displaystyle 900$ and $\displaystyle 1100$ hours; $\displaystyle 1150$ never occurs among them. \[P(\text{life}=1150\text{ h}) = \frac{0}{80} = 0 \]

  10. Exercise 30

    Refer to Q. 29\displaystyle 29 above : The probability that bulbs selected randomly from the lot has life less than 900\displaystyle 900 hours is : (A) 1140\displaystyle \frac{11}{40} (B) 516\displaystyle \frac{5}{16} (C) 716\displaystyle \frac{7}{16} (D) 916\displaystyle \frac{9}{16}

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    NCERT’s answer
    (D)
    (D) \(\displaystyle \frac{9}{16}\) \[P(\text{life}<900) = \frac{10+12+23}{80} = \frac{45}{80} = \frac{9}{16} \]Answer: \(\displaystyle \dfrac{9}{16}\).