Statistics - Test Papers

 CBSE Test Paper 01

CH-14 Statistics


  1. Which of the following variables are discrete ? 1. Size of shoes, 2. Number of pages in a book, 3. Distance travelled by a train, 4. Time
    1. 2 and 4
    2. 1 and 3
    3. 1 and 4
    4. 1 and 2
  2. ‘Less than’ cumulative frequency table for a given data is as follows. Then, the frequency of class interval 20-30 is
    MarksLess than 10Less than 20Less than 300Less than 40
    Cumulative frequency3173792
    1. 34
    2. 55
    3. 14
    4. 20
  3. Find out the mode of the following: 5, 4, 3, 5, 6, 6, 6, 5, 4, 5, 5, 3, 2, 1
    1. 4
    2. 5
    3. 6
    4. 3
  4. In the given graph, the number of students who scored 60 or more marks is
    1. 22
    2. 20
    3. 21
    4. 19
  5. In a bar graph if 1 cm represents 30 km, then the length of bar needed to represent 75 km is
    1. 3.5 cm
    2. 2.5 cm
    3. 2 cm
    4. 3 cm
  6. Fill in the blanks: The difference between the upper-class limit and lower class limit is called ________ .
  7. Fill in the blanks: The percentage of marks obtained by students of a class in mathematics are 65, 35, 37, 23, 0, 18, 82, 92, 72, 32, 10, 5. Then median is ________. 
  8. Write the class mark of 90-110 group.
  9. Find the arithmetic mean of first 6 natural numbers.
  10. Find the median of the following observation : 72, 68, 42, 33, 35, 39, 40, 41, 65, 69
  11. The mean of 40 observations was 160. It was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean. Find the correct mean.
  12. Draw a histogram and frequency polygon to represent the following data on the same scale) which shows the monthly cost of living index of a city in a period of 2 years :

    Cost of living index

    Number of months

    440-460

    2

    460-480

    4

    480-500

    3

    500-520

    5

    520-540

    3

    540-560

    2

    560-580

    1

    580-600

    4

    Total

    24

  13. Find the missing value of p of the following distribution whose mean is 12.58.

    x581012p2025
    f25822742
  14. The water bills (in Rs.) of 32 houses in a certain street for the period 1.1.98 to 31.3.98 are given below:
    56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59.
    Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals.

  15. Find the missing frequencies in the following frequency distribution if it knows that the mean of the distribution is 50. The total frequency is 120. 

    x1030507090
    f17f132f219

CBSE Test Paper 01
CH-14 Statistics


Solution

  1. (d) 1 and 2
    Explanation: Discrete variables are variables that can only take finite values.

    Size of shoes & pages in the book have finite number.

  2. (d) 20
    Explanation: A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.

    Less than 30 has the class interval 20-30. Frequency of this class interval will be corresponding to

    MarksCumulative
    frequency
    ClassFrequency
    Less than 1031-103
    Less than 201710-2014
    Less than 303720-3020
    Less than 409230-4055

    37 - 17 = 20

  3. (b) 5
    Explanation: The observation which occurs maximum number of times is called as mode of the given data.

    Above given data has maximum number of 5, so mode is 5

  4. (c) 21
    Explanation: Add the values corresponding to the height of the bar from 60 to 100

    10 + 5 + 3 + 3 = 21

  5. (b) 2.5 cm
    Explanation: 1 cm - 30 km

    so  for 75 km

     7530=2.5cm

  6. class width/ class size

  7. 33.5

  8. Class Mark = Upper class Limit+Lower Class Limit2

    Class Mark = 110+902

    Class Mark = 2002

    Class Mark = 100

  9. First six natural numbers are 1, 2, 3, 4, 5, 6. Let X¯ be their arithmetic mean. Then,
    X¯ = 1+2+3+4+5+66 = 216 = 72 = 3.5 

  10. Arranging the data in ascending order, we have
    33, 35, 39, 40, 41, 42, 65, 68, 69, 72
    Number of items (N) = 10 which is even.
    Median=Sizeof(N2)thitem+Sizeof(N2+1)thitem2
    =Sizeof5thitem+Sizeof6thitem2
    =41+422=41.5.

  11. Here, n = 40, X¯ = 160
    So, X¯ = 1n(xi 160 = 140(xi xi = 160 × 40 = 6400
     Incorrect vlaue of xi = 6400
    Now,
    Correct value of xi = Incorrect value of xi - Incorrect item + Correct item
     Correct value of xi = 6400 - 125+165 = 6440
     Correct mean = Correct value of xin = 644040 = 161

  12. Histogram and Frequency polygon representing the cost of living index of a city in a period of 2 years.

  13. xififixi
    5210
    8540
    10880
    1222264
    p77p
    20480
    25250
     N = 50fixi = 7p + 524

    Given  Mean = 12.58
     fixiN = 12.58
     7p+52450 = 12.58
     7p + 524 = 629
     7p = 629 - 524
     7p = 105
     p = 1057 = 15

  14. The minimum and maximum bills are Rs.24 and Rs.95.
    The range is 95 - 24 = 71
    Given class interval is 70 - 79. So, class size is 79 - 70 = 9
     Number of classes = RangeClasssize = 719 = 7.80
     Number of classes = 8
    The cumulative frequency distribution is as:

    Bills (Rs.)No. of house (Frequency)Cumulative frequency
    16-2511
    25-3434
    34-4359
    43-52413
    52-61720
    61-70626
    70-79329
    79-88231
    88-97132
  15. xififixi
    1017170
    30f130f1
    50321600
    70f270f2
    90191710
     N = 120fixi = 3480 + 30f1 + 70f2

    Given, Mean = 50
     fixiN = 50
     30f1+70f2+3480120 = 50
     30f1 + 70f2 + 3480 = 6000
     30f1 + 70f2 = 6000 - 3480
     30f1 + 70f2 = 2520
     3f1 + 7f2 = 252 ....(i) [Divide by 10]
    And N = 120
     17 + f1 + 32 + f2 + 19 = 120
     68 + f1 + f2 = 120
     f1 + f2 = 120 - 68 = 52
     3f1 + 3f2 = 156 ...(ii) [Multiply by 3]
    Subtract equation (ii) from equation (i),
    3f1 + 7f2 - 3f1 - 3f2 = 252 - 156
     4f2 = 96
     f2 = 964 = 24
    Put value of f2 in equation (i),
    3f1 + 7 × 24 = 252
     3f1 + 168 = 252
     3f1 = 252 - 168 = 84
     f1 = 843 = 28