10th Class Mathematics Statistics Question Bank

done Statistics and Probability Total Questions - 40

• question_answer1)
  By constructing a cumulative frequency table, we can use it in determining the _______
  A)
  mean    done clear
  B)
                 mode done clear
  C)
   median     done clear
  D)
   mean and mode done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer2)
  If n is the total number of observation, then the class whose cumulative frequency is greater than (and nearest to) \[\frac{\mathbf{n}}{\mathbf{2}}\] is called the ________ 
  A)
  modal class done clear
  B)
   median class done clear
  C)
    class preceding the modal class done clear
  D)
   Class preceding the median class done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer3)
  Which among the following statements is incorrect?
  A)
  In a grouped frequency distribution/ it is not possible to determine the mode by looking at the frequencies, done clear
  B)
    In a grouped frequency distribution, modal class is the class which have maximum frequency. done clear
  C)
   The mode of the data is a value inside the modal class done clear
  D)
   Median of the grouped data can be calculated by using the formula. Median =\[l+\left( \frac{\frac{n}{2}-cf}{f} \right)\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer4)
  If a mode exceeds a mean by 15 then the mode exceeds the median by________
  A)
  15           done clear
  B)
   10           done clear
  C)
   5                                                                     done clear
  D)
   20 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer5)
  If x < y < 2x and the mean and the median of x, y and 2x are 18 and 15 respectively, then the value of x is ______
  A)
  10                                                                     done clear
  B)
   11           done clear
  C)
   12                                                                    done clear
  D)
   13 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer6)

  Directions: Consider the following distribution table:
  Class interval	0-8	8-16	16-24
  Frequency	3	5	8

  Find the coefficient of variation for the above distribution.
  A)
  20.29                                                    done clear
  B)
   42.76         done clear
  C)
   40.82                                                               done clear
  D)
   48.68 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer7)

  Directions: Consider the following distribution table:
  Class interval	0-8	8-16	16-24
  Frequency	3	5	8

  Find the variance of the given distribution
  A)
  37.88                                                                done clear
  B)
   42.39         done clear
  C)
   48.76        done clear
  D)
   45.2 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer8)
  If A, B, C are respectively the mean, median and mode of a data such that A: B = 4: 3, then find the ratio of B : C.
  A)
  3 : 1         done clear
  B)
   1 : 2         done clear
  C)
   2 : 1                             done clear
  D)
   3 : 4 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer9)
  Find the mean of the data a, a + m, a + 2m, a + 3m, ____ up to (2n + 1) terms
  A)
  \[a+nm+1\]       done clear
  B)
   \[a+nm\]       done clear
  C)
    \[a+2nm\]                   done clear
  D)
   \[a+2mn-1\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer10)

  Find the variance of the data

  3, 10, 17, _____199

  A)
  2125                 done clear
  B)
          3430         done clear
  C)
   5120                done clear
  D)
   7290 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer11)
  Find the median of the first m terms of the data whose \[{{\mathbf{n}}^{\mathbf{th}}}\]term is 2n + 1.
  A)
  \[2m\]                                                    done clear
  B)
   \[2m-1\]       done clear
  C)
   \[m\]                            done clear
  D)
   \[2m+3\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer12)
  Find the median of the data \[\mathbf{a,}\,\,\mathbf{ar,}\,\,\mathbf{a}{{\mathbf{r}}^{\mathbf{2}}}\mathbf{,}\] ______, \[\mathbf{a}{{\mathbf{r}}^{\mathbf{n}}}\]where n is an odd number.
  A)
  \[\frac{a}{2}(1+r)\,{{r}^{\frac{n+1}{2}}}\]                                                      done clear
  B)
   \[\frac{a}{2}(1-r)\,{{r}^{\frac{n+1}{2}}}\] done clear
  C)
   \[\frac{a}{2}(1+r)\,{{r}^{\frac{n-1}{2}}}\]                                                       done clear
  D)
   \[\frac{a}{2}(1-r)\,{{r}^{\frac{n-1}{2}}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer13)
  For a given frequency distribution, median can be found graphically with the help of
  A)
  histogram                       done clear
  B)
   ogive done clear
  C)
   frequency curve             done clear
  D)
   frequency poiygon done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer14)
  Which among the following statements is correct?
  A)
  Mode is the middle most value of a data. done clear
  B)
   Median and mode of a data can be determined graphically. done clear
  C)
   The mode of a frequency distribution can be determined graphically from ogive. done clear
  D)
   All the above done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer15)
  The following data gives the distribution of total household expenditure (in rupees) on cable connections in a city.

  Expenditure (in RS.)	Frequency
  1000\[-\]1500	14
  1500\[-\]2000	30
  2000\[-\]2500	23
  2500\[-\]3000	18
  3000\[-\]3500	20
  3500\[-\]4000	12

  Find the average expenditure which is being done on the maximum number of cable connection.
  A)
  Rs. 1847.83                                                       done clear
  B)
   Rs. 1648.26 done clear
  C)
   Rs. 2025.38                                                      done clear
  D)
   Rs. 1918.35 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer16)
  \[\frac{\mathbf{x}}{\mathbf{3}}\mathbf{,}\frac{\mathbf{x}}{\mathbf{2}}\mathbf{,}\frac{\mathbf{x}}{\mathbf{4}}\]\[\mathbf{,}\frac{\mathbf{3x}}{\mathbf{4}}\mathbf{,}\frac{\mathbf{2x}}{\mathbf{5}}\mathbf{,}\]\[\mathbf{x,}\frac{\mathbf{2x}}{\mathbf{3}}\mathbf{,}\frac{\mathbf{x}}{\mathbf{5}}\] are the observations of a data such that x > 0. If  the median of the data is 18, then find the value of x.
  A)
  15                                                                     done clear
  B)
   25           done clear
  C)
   40                                                                    done clear
  D)
   35 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer17)
  p < q < r < s and p, q, r, s are non zero integers. If mean and median of p, q, r, s are 10 and 9 respectively then which one of the following statements can be true?
  A)
  p = 10 and s =12                                              done clear
  B)
   q = 6 and r = 12 done clear
  C)
   p = 8 and s =14                                               done clear
  D)
   All the above done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer18)
  The upper quartile of the data 8, 15, 17, 9, 7, 5 is _________
  A)
  9                                                                      done clear
  B)
   10           done clear
  C)
   12                                                                    done clear
  D)
   15 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer19)
  If the median of the following frequency distribution is 28.5 then the values of f1 and f2 are respectively _______

  Class interval	0-10	10-20	20-30	30-40	40-50	50-60	Total
  Frequency	5	F1	20	F2	8	5	60

  A)
  9 and 13                                                            done clear
  B)
   7 and 15      done clear
  C)
   8 and 14                                                           done clear
  D)
   7 and 13 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer20)
  If the mean of the following distribution is 54, then find the value of f.

  Class-interval	0-20	20-40	40-60	60-80	80-100
  frequency	7	11	10	f	13

   
  A)
  6                                                                      done clear
  B)
   7            done clear
  C)
   8                                                                     done clear
  D)
   9 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer21)
  Compute the median for the following cumulative frequency distribution:

  Mark obtained	Cumulative frequency
  More than or equal to 20	100
  More than or equal to 30	96
  More than or equal to 40	84
  More than or equal to 50	70
  More than or equal to 60	54
  More than or equal to 70	34
  More than or equal to 80	18
  More than or equal to 90	8
  More than or equal to 100	0

  A)
  60                                                         done clear
  B)
   55           done clear
  C)
   58                                                                    done clear
  D)
   62 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer22)
  If three unbiased coins are tossed together, then the probability of getting at least two heads is ____
  A)
  \[\frac{1}{3}\]                                                               done clear
  B)
   \[\frac{1}{8}\]           done clear
  C)
   \[\frac{1}{2}\]                                                              done clear
  D)
   \[\frac{1}{4}\] done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer23)
  A bag contains 11 red bails and some white balls. If the probability of drawing a white ball is double that of a red ball, then the number of white ball in the bag is ________
  A)
  20                                                                     done clear
  B)
   11           done clear
  C)
   22                                                                    done clear
  D)
   28 done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer24)
  A number p is selected from the numbers 1, 3, 5 and then a second number q is randomly selected from the numbers 1, 6, 9. What is the probability that the product pq of the two numbers will be less than 20?
  A)
  \[\frac{1}{9}\]                                                               done clear
  B)
   \[\frac{4}{3}\]            done clear
  C)
   \[\frac{2}{3}\]                                                              done clear
  D)
   \[\frac{7}{9}\] done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer25)
  The times (in seconds) taken by 72 atheletes to run a 200 m hurdle race are tabulated below:

  Class	15.2\[-\]15.4	15.4\[-\]15.6	15.6\[-\]15.8	15.8\[-\]16.0
  Frequency	13	19	23	17

  If an athelete is chosen at random, then find the probability that he is the one who has completed the race in less than 15.8 seconds.
  A)
  \[\frac{55}{72}\]                                                            done clear
  B)
   \[\frac{23}{72}\]           done clear
  C)
    \[\frac{1}{4}\]                                                             done clear
  D)
   \[\frac{17}{72}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer26)
  Which of the following cannot be the probability of an event?
  A)
  0.001                                                                done clear
  B)
   \[\frac{3}{4}\]            done clear
  C)
   1%                                                                   done clear
  D)
   \[\frac{9}{8}\] done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer27)
  Two dice are thrown randomly. Find the probability of getting a doublet or a total of 8.
  A)
  \[\frac{3}{8}\]                                                               done clear
  B)
   \[\frac{5}{18}\]           done clear
  C)
   \[\frac{1}{6}\]                                                              done clear
  D)
   \[\frac{2}{9}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer28)

  Directions: In a game, the entry fee is Rs. 20. In the game, a coin is tossed 3 times. On showing two tails, swapnesh gets his entry fee back. If he throws 3 tails, he receives double the entry fees. Otherwise he will lose. If he tossed a coin three times, then ______

  Find the probability that, he loses the entry fee.
  A)
  \[\frac{1}{2}\]                                                               done clear
  B)
   \[\frac{1}{4}\]           done clear
  C)
   \[\frac{3}{8}\]                                                              done clear
  D)
   \[\frac{1}{8}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer29)

  Directions: In a game, the entry fee is Rs. 20. In the game, a coin is tossed 3 times. On showing two tails, swapnesh gets his entry fee back. If he throws 3 tails, he receives double the entry fees. Otherwise he will lose. If he tossed a coin three times, then ______

  Find the probability that, he gets double entry fee.
  A)
  \[\frac{3}{4}\]                                                               done clear
  B)
   \[\frac{1}{8}\]             done clear
  C)
   \[\frac{1}{2}\]                                                              done clear
  D)
   \[\frac{3}{8}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer30)

  Directions: In a game, the entry fee is Rs. 20. In the game, a coin is tossed 3 times. On showing two tails, swapnesh gets his entry fee back. If he throws 3 tails, he receives double the entry fees. Otherwise he will lose. If he tossed a coin three times, then ______

  Find the probability that, he just gets her entry fee.
  A)
  \[\frac{1}{8}\]                                                                           done clear
  B)
   \[\frac{1}{4}\] done clear
  C)
   \[\frac{3}{8}\]                                                                          done clear
  D)
   \[\frac{1}{2}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer31)

  Directions: The king, queen and ace of clubs are removed from a deck of 52 playing cards and then

  well shuffled. Now on drawing a card at random from the remaining cards, then ______

  Find the probability that, the card is a king of black colour.
  A)
   \[\frac{1}{13}\]                                                                         done clear
  B)
    \[\frac{13}{49}\]           done clear
  C)
   \[\frac{1}{49}\]                                                             done clear
  D)
   \[\frac{1}{2}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer32)

  Directions: The king, queen and ace of clubs are removed from a deck of 52 playing cards and then

  well shuffled. Now on drawing a card at random from the remaining cards, then ______

  Find the probability that, the card is either an ace or a jack.
  A)
  \[\frac{1}{7}\]                                                               done clear
  B)
  \[\frac{3}{49}\]           done clear
  C)
   \[\frac{4}{49}\]                                                             done clear
  D)
   \[\frac{8}{49}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer33)
  A card is drawn at random from a well shuffled deck of cards. The probability that it is a face card of diamonds, is ______
  A)
  \[\frac{3}{13}\]                                                  done clear
  B)
    \[\frac{1}{13}\]           done clear
  C)
   \[\frac{1}{26}\]                                                             done clear
  D)
   \[\frac{3}{52}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer34)
  A three digit number is to be formed by using the digits 1, 5, 6, 8 and 9 without repetition. The probability that it is an even number, is ________
  A)
  \[\frac{1}{5}\]                                                                           done clear
  B)
   \[\frac{2}{5}\]                                      done clear
  C)
   \[\frac{3}{5}\]                                      done clear
  D)
   \[\frac{4}{5}\]                                                  done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer35)
  If a number is selected at random from the first 20 natural numbers, then find the probability that it is not a prime number
  A)
   \[\frac{1}{5}\]        done clear
  B)
   \[\frac{3}{5}\]           done clear
  C)
    \[\frac{2}{5}\]                                                             done clear
  D)
   \[\frac{4}{5}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer36)
  Two dice are thrown. Find the probability of getting a total of 10 or 12?
  A)
  \[\frac{1}{9}\]                                                               done clear
  B)
   \[\frac{2}{9}\]            done clear
  C)
   \[\frac{3}{4}\]                                                              done clear
  D)
   \[\frac{1}{3}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer37)
  If the probability of happening of rain on a day is 0.75 then find the probability of non-happening of rain.
  A)
  \[\frac{1}{2}\]    done clear
  B)
                                                          \[\frac{1}{3}\]             done clear
  C)
   \[\frac{1}{4}\]                                                              done clear
  D)
   \[\frac{1}{5}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer38)

  Directions: In a bag there are n balls out of which \[\frac{\mathbf{n}}{\mathbf{4}}\] balls are black, \[\frac{\mathbf{n}}{\mathbf{8}}\] balls are white and \[\frac{\mathbf{5n}}{\mathbf{8}}\]

  balls are red. A ball is drawn at random from the bag.

  The probability that the drawn ball is either black or red, is _________
  A)
  \[\frac{7}{8}\]                                                                           done clear
  B)
   \[\frac{7n}{4}\] done clear
  C)
   \[\frac{5n}{2}\]                                                             done clear
  D)
   \[\frac{1}{8}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer39)

  Directions: In a bag there are n balls out of which \[\frac{\mathbf{n}}{\mathbf{4}}\] balls are black, \[\frac{\mathbf{n}}{\mathbf{8}}\] balls are white and \[\frac{\mathbf{5n}}{\mathbf{8}}\]

  balls are red. A ball is drawn at random from the bag.

  The probability that the drawn ball is of white colour is ____
  A)
  \[\frac{n}{2}\]                                                               done clear
  B)
   \[\frac{1}{4}\] done clear
  C)
   \[\frac{1}{8}\]                                                              done clear
  D)
   \[\frac{3n}{4}\] done clear
  E)
    None of these done clear
  View Solution play_arrow

• question_answer40)

  Directions: In a bag there are n balls out of which \[\frac{\mathbf{n}}{\mathbf{4}}\] balls are black, \[\frac{\mathbf{n}}{\mathbf{8}}\] balls are white and \[\frac{\mathbf{5n}}{\mathbf{8}}\]

  balls are red. A ball is drawn at random from the bag.

  The probability that the drawn ball is neither white nor red, is_________
  A)
  \[\frac{n}{2}\]                                                               done clear
  B)
    \[\frac{n}{4}\] done clear
  C)
   \[\frac{1}{2}\]                                                                          done clear
  D)
   \[\frac{1}{4}\] done clear
  E)
   None of these done clear
  View Solution play_arrow