Statistics MCQ Class 9 CBSE | Maths

Mathematics Chapter 14 Statistics MCQ  for CBSE Class 9.

1.   In the following data,

The actual exclusive class limits of the fourth class are

(A) 45–50                                                        

(B) 44.5–49.5

(C) 44.5–48.5                                                  

(D) 43.5–48.5

Ans.     (B)

Sol.      The actual exclusive class limits of the fourth class are : 44.5 – 49.5

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2.    A histogram is a n-dimensional diagram where n is equal to :

(A) 0    

(B) 1

(C) 2    

(D) 3    

Ans.     (C)

Sol.      A histrogram is two dimensional diagram.

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3.   If the class intervals in a frequency distribution are 72-73.9, 74-75.9, 76-77.9, 78-79.9 etc. then the mid point of class 74-75.9 is :

(A) 74.5

(B) 74.9

(C) 74.95                                                         

(D) 75.00                                                        

Ans.     (C)

Sol.      The mid point of  74 – 75.9 is 74.95

Following marks were obtained by 12 students in a mathematics test :

21, 20, 25, 5, 10, 15, 30, 12, 7, 16, 9, 22

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4.   The range of the marks is :

(A) 20  

(B) 25

(C) 21  

(D) 7    

Ans.     (B)

Sol.      Range = 30 – 5 = 25

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5.   For the following table :

The upper limit of the class interval 15–20 is :

(A) 15  

(B) 20  

(C) 25  

(D) 22  

Ans.     (B)

Sol.      The upper limit of the class interval 15–20 is 20.

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6.    For the following table, find the class mark for frequency distribution of ‘10’?

(A) 52  

(B) 31

(C) 21  

(D) 26

Ans.     (D)

Sol.      The class mark for frequency distribution of 10 is 26.

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7.   If mean of 121 numbers is 59. If each number is multiplied by 4. What will be the new mean?

(A) 234 

(B) 235

(C) 236 

(D) 237

Ans.     (C)

Sol.      Mean will also be 4 times

    ⇒         4 × 59 = 236

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8.  The class marks of a distribution are :

47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102

Answer the following question :

What is class size?

(A) 4    

(B) 6

(C) 5    

(D) 7

Ans.     (C)

Sol.      Class size will be 5

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9.   The class marks of a distribution are :

47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102

Answer the following question :

What are class limits?

(A) 44.5, 49.5                                                  

(B) 43.5, 48.5

(C) 45.5, 50.5                                                  

(D) 41.5, 47.5

Ans.     (A)

Sol.      Class limits will be 44.5, 49.5

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10.  The class marks of a distribution are :

47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102

Answer the following question :

What are true class limits?

(A) 44.5, 49.5                                                  

(B) 43.5, 48.5

(C) 45.5, 50.5                                                  

(D) 41.5, 47.5

Ans.     (A)

Sol.      True class limits will be 44.5 , 49.5

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11.   In an examination 10 students scored marks in mathematics 35, 19, 28, 32, 63, 02, 47, 31, 13, 98 its range is :

(A) 96                                      

(B) 02

(C) 98                                      

(D) 50

Ans.     (A)

Sol.      Here minimum mark is = 02

                    maximum mark is  = 98

                      Range = 98 – 02 = 96

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12.   The following is the distribution of weight (in kg) of 52 persons :

Weight in kg :	30 -40	40 – 50	50 – 60	60 – 70	70 – 80
No of Persons :	10	15	17	6	4

What is the class size :(A) 12                                      

(B) 11

(C) 10                                      

(D) 9

Ans.     (C)

Sol.      Upper limit – Lower limit  = class size

              \Rightarrow Class size is 10.

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13.   The difference between the maximum and the minimum observations in the data is called :

(A) Class interval                                            

(B) Frequency                         

(C) Cummulative frequency      

(D) Range

Ans.     (D)

Sol.      Range

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14.   If (1 – 100), (101 – 200), (201 – 300) etc. are the class intervals of a frequency distribution, then the true class width is :

(A) 99                                      

(B) 99.5

(C) 100                                     

(D) 100.5

Ans.     (C)

Sol.      True class width   = 100

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15.   Angle of the sector for each variable is known as :

(A) Adjacent angle                                         

(B) Right angle                        

(C) Central angle                                            

(D) Supplementary angle         

Ans.     (C)

Sol.      Angle of the sector for each variable, is known as central angle.

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16.      

The percentage of students in science faculty in 1990-91 is :

(A) 26.9%                                                      

(B) 27.8%

(C) 29.6%                                                      

(D) 30.2%

Ans.     (C)

Sol.      Total student in 1990-91

            = 600 + 400 + 200 + 150

            = 1350

            In science = \frac{{400}}{{1350}} × 100 = 29.62%       

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17. 

The percentage of students in law faculty in 1992-93 is :

(A) 18.5%                                                      

(B) 12.9%

(C) 16.7%                                                      

(D) 14.8%

Ans.     (B)

Sol.      Total students in 1992-93

            = 550 + 600 + 200 + 200

            = 1550

             In law faculty = \frac{{200}}{{1550}} \times \,100\,\, = \,\,12.90\%

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18.   

How many times (Approximate) was the total strength that of the commerce students in 1991-92 ?

(A) 3 times                                                     

(B) 4 times

(C) 5 times                                                     

(D) 6 times

Ans.     (D)

Sol.      Total strength in 1991-92 = 550 + 500 + 250 + 150

                                                     = 1450

                     Commerce student  = 250

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19.   

During which year the strength of students in arts faculty was minimum :

(A) 1990-91                                                    

(B) 1991-92

(C) 1992-93                                                    

(D) Both (B) and (C)

Ans.     (D)

Sol.      In 1991-92 and 1992-93  art students strength was = 550

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20.   

How much percent was the increase in science students in 1992-93 over 1990-91 ?

(A) 50%                                                         

(B) 150%

(C) 66\frac{2}{3}\%                    

(D) 75%

Ans.     (A)

Sol.      In  1990-91 science students = 400

            In 1992-93 science students = 600

           increase = 200

           50% increease

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21. 

A regular increase in no. of students was in the faculty of :

(A) Law                                           

(B) Science

(C) Commerce                                                 

(D) Arts

Ans.     (B)

Sol.      Science

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22.   Histogram is useful to determine graphically the value of :

(A) Arithmetic Mean                                         

(B) Median

(C) Mode                                                        

(D) None of these

Ans.     (C)

Sol.      Mode

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23.   In any -chart, the sum of the central angles is :

(A) 90°                                            

(B) 180°

(C) 270°                                                          

(D) 360°

Ans.     (D)

Sol.      360º

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24.   The frequency polygon for the distribution.

Class interval	0 – 3	3 – 6	6 – 9	9 – 12	12 – 15
Frequency	2	4	5	3	2

(A)                                                  

(B)   

(C)                                                  

(D)     

Ans.     (C)

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25.   Which one of the following groups has different class interval from others ?

(A) 120 – 125                                                  

(B) 243 – 249                                 

(C) 141.5 – 146.5                                             

(D) 315.5 – 320.5 

Ans.     (B)

Sol.      243 – 249 has class interval  = 6

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26.   Refer the figure given below answer the following question.

What is frequency of the class – interval 20 – 30 ?

(A) 25                                             

(B) 20

(C) 5                                               

(D) 10

Ans.     (B)

Sol.      Frequency of the class-interval 20-30 is 20.

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27.   Refer the figure given below answer the following question.

How many class – interval have equal frequency ?

(A) 2                                               

(B) 3

(C) 1                                               

(D) None of these

Ans.     (A)

Sol.      Class interval 10-20 and 40-50 have equal frequency.

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28.   Refer the figure given below answer the following question.

What is the cumulative frequency of the interval 40 – 50 ?

(A) 70                                                 

(B) 60

(C) 50                                                 

(D) 80

Ans.     (D)

Sol.      Cumulative frequency of the interval 40-50 is 15 + 10 + 20 + 25 + 10 = 80.

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29.   Study the following graph and answer the question given below :

To show the distribution of proteins and other dry elements in the human body, the arc of the circle should subtend at the centre an angle of :

(A) 126^o                                          

(B) 54^o                                           

(C) 108^o                                                          

(D) 252^o 

Ans.     (C)

Sol.      The area of the circle = = 108º.

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30.   If (11-15), (16-20), (21-25), (26-30) etc. are the class interval of a frequency distribution, then the true class width is :

(A)  4                                              

(B) 4.5

(C)  5                                              

(D)  5.5

Ans.     (C)

Sol.      True class width is 5.

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31.   The mean of 7 numbers is 13 and the mean of 13 other numbers is 7. What is the mean of all 20 numbers :

(A) 9.1                                           

(B) 18.2

(C) 9.37                                          

(D) 10

Ans.     (A)

Sol.      Mean of all 20 numbers = \frac{{(13 \times 7) + (7 \times 13)}}{{7 + 13}}

            = \frac{{182}}{{20}} = 9.1   

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32.    A group of 10 items has mean 6. If the mean of 4 of these items is 7.5, then the mean of the remaining items is :

(A) 6.5                                           

(B) 5.5

(C) 4.5                                           

(D) 5.0

Ans.     (D)

Sol.      Mean of the remaining items = \frac{{(10 \times 6) - (4 \times 7.5)}}{6}

                                                      = \frac{{30}}{6} = 5

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33.   Mode of the distribution :

is :

(A) 6                                              

(B) 10

(C) 8                                              

(D) None of these

Ans.     (A)

Sol.      6 marks has highest frequency.

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34.   Which of the following statements is not true

(A) Mean is affected by extreme values but median is not

(B) Mean and median are both affected by extreme values.

(C) We can find mean for quantitative data only.

(D) Median can be found for quantitative as well as qualitative data.

Ans.     (B)

Sol.      Mean and median are both not affected by extreme values.

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35.    The relationship between mean, median and mode for a moderately skewed distribution is

(A) mode = median – 2 mean         

(B) mode = 2 median –  mean

(C) mode = 2 median  –  3 mean    

(D) mode = 3 median – 2 mean

Ans.     (D)

Sol.      Mode = 3 median – 2 mean

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36.   The mean of first three is 14 and mean of next two terms is 18. The mean of all the five terms is :

(A) 14.5                                                         

(B) 15.0

(C) 15.2                                          

(D) 15.6

Ans.     (D)

Sol.      {x_1}\, + \,.....{x_3}\, = \,42

            {x_4}\, + \,{x_5}\, = \,36

            {x_1}\, + \,.....{x_5}\, = \,78

            \bar x\, = \,\frac{{78}}{5}\, = \,15.6

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37.    If the mode of a data is 18 and the mean is 24, then median is :

(A) 18                                            

(B) 24

(C) 22                                            

(D) 21

Ans.     (C)

Sol.      Mode = 3 median – 2 mean

            18 = 3 median – 2 × 24

            Median = \frac{{66}}{3}= 22

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38.    The mean of 5 data has been wrongly found to be 45 due to the fact that one of the data has been wrongly taken as 50 instead of 40. Then the correct mean will be :

(A) 40                                                

(B) 43

(C) 44                                                

(D) 46

Ans.     (B)

Sol.      Correct mean = \frac{{(5 \times 45) - 50 + 40}}{5}

            = 45 – 2 = 43       

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39.    In an arranged discrete series in which total number of observations ‘n’ is even, median is

 (A)  \frac{n}{2}th\,\,item           

(B)   \left( {\frac{n}{2} + 1} \right)th\,\,\,item

(C) the mean of \frac{n}{2}th and \left( {\frac{n}{2} + 1} \right)th\,\,\,item

(D) None of these

Ans.     (C)

Sol.      Median = \frac{{{{\left( {\frac{n}{2}} \right)}^{th}}\, + \,{{\left( {\frac{{n\, + 1}}{2}} \right)}^{th}}term}}{2} . [If n is even]

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40.   The median of the data 25, 34, 31, 23, 22, 26, 35, 29, 20, 32 is :

(A) 27                                            

(B) 26.5

(C) 28.5                                          

(D) None of these

Ans.     (D)

Sol.      20, 22, 23, 25, 26, 29, 31, 32, 34, 35

         median  = \frac{{26 + 29}}{2}

                        = 27.5 is the median.

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41.   If the mean of five observations x, x + 2, x + 4, x + 6, x + 8, is 11, then the mean of the first three observations is :

(A) 9                                          

(B) 11

(C) 13                                        

(D) None of these

Ans.     (A)

Sol.          x+x+2+x+4+x+6+x+8  = 55

                                     5x + 20  = 55

                                             5x  = 35

                                              x  = 7

            Number are 7, 9, 11, 13, 15

            Mean of first there numbers are

            = \frac{{7\, + \,9\, + \,11}}{3}\, = \,\frac{{27}}{3}\, = \,9

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42.    If the arithmetic mean of 5, 7, 9, x is 9 then x = :

(A) 11                                        

(B) 15

(C) 18                                        

(D) 16

Ans.     (B)

Sol.      5 + 7 + 9 + x = 36

            x = 36 – 21

            x = 15     

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43.   If the first 5 elements of a set of observations and next five elements are replaced by x_i + 5, i = 1,2,3, …, 5 and  x_i – 5, i = 6,7,…10 respectively then the mean will change by :

(A) 25                                        

(B) 10

(C) 5                                          

(D) 0  

Ans.     (D)

Sol.      x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉, x₁₀

                First five replaced by

            x₁+5, x₂+5, x₃+5, x₄+5, x₅+5

            Last five replaced by:

            x₆–5,  x₇–5 , x₈–5, x₉–5, x₁₀–5

            here mean will be remain unchanged as sum of observations is as it is.

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44.   If the mean and median of a set of numbers are 8.9 and 9 respectively, then the mode will be :

(A) 7.2                                       

(B) 8.2

(C) 9.2                                       

(D) 10.2

Ans.     (C)

Sol.      Mode = 3 median – 2 mean

            = 3 × 9 – 2 × 8.9

            = 27 – 17.8

            Mode = 9.2

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45.   The mean of 10 sets of observations is 12 and that of another 12 sets of observations is 10. Then the mean for the combined set of observations is :

(A) 10                                        

(B) 10.909

(C) 12                                        

(D) 60

Ans.     (B)

Sol.      Mode = \frac{{{x_1}\, + \,..........{x_{10\,}} + \,{x_{11\,}}\, + \,..... + \,{x_{22}}}}{{22}}

            = \frac{{120\, + \,120}}{{22}} = \frac{{240}}{{22}} = 10.909

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46.   The average weight of 10 men is decreased by 3 kg when one of them whose weight is 80 kg is replaced by a new person. The weight of the new person is :

(A) 70                                        

(B) 60

(C) 50                                        

(D) 73

Ans.     (C)

Sol.      Let         x₁ + ……… + x₁₀  = 10\,\bar x

           x₁ + ……….. + x₉ + 80 = 10\,\bar x                

           x₁ + ………….+ x₉ + x₁₀   = 10(\bar x\, - \,3) [Let weight of new person is x₁₀ kg]                                                         10\,\bar x\, - \,80\, + \,{x_{10}}   = 10\,\bar x – 30

            x₁₀  = 80 – 30

                   = 50 kg

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47.   Average scores of 50 students in a class is 44. Later on it was found that a score 23 was incorrectly recorded as 73. The correct average score is :

(A) 42                                        

(B) 43

(C) 45                                        

(D) 44

Ans.     (B)

Sol.      Now correct mean = 44 + \frac{{23 - 73}}{{50}}

                                           = 43

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48.    Kavita obtained 16, 14, 18 and 20 marks (out of 25) in Maths in weekly tests in the month of Jan 2000 ; then mean marks of Kavita is :

(A) 16                                        

(B) 16.5

(C) 17                                        

(D) 17.5

Ans.     (C)

Sol.      Mean marks = \frac{{16\, + \,14\, + \,18\, + 20}}{4}

            = \frac{{68}}{4} = 17

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49.    The mode of the distribution 1,2,3,4,4,4,5,7 is :

(A) 7                                          

(B) 4

(C) 3                                          

(D) 1

Ans.     (B)

Sol.      4 has highest no. of frequency

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50.   The median of first 12 prime numbers is :

(A) 19                                        

(B) 12

(C) 15                                        

(D) 17

Ans.     (C)

Sol.      2, 3, 5, 7, 11, 13, 17, 19, 23,  29, 31, 37

            median = \frac{{13 + 17}}{2} = 15

 

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