Math class IX statistic

                                               Statistic

                                              Class IX-Mathematics

                                               MISCELLANEOUS

1.The class marks of distribution are: 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102. Determine the class

   size, the class limits and the true class limits.

2. Find the range of the following array of data: 70, 65, 71, 36, 55, 61, 62, 41, 40, 39, 35.

3. The electricity bills (in rupees) of 41 houses in a locality are given below. Construct a frequency

    distribution table with a class size of 10.

    30, 35, 37, 28, 32, 34, 40, 50, 47, 46, 55, 52, 44, 43, 44, 45, 61, 60, 59, 25, 26, 27, 48, 49, 50, 41, 42,      43,57, 58, 56, 55, 60, 70, 72, 69, 88, 89, 101, 103, 99.

4.The class marks of a distribution are 105, 115, 125, 135, 145, 155, 165, 175. Find the class size and

   class limits

5.There are 50 students in a class of which 40 are boys and the rest are girls. The average weight of

   the class is 44 kg and the average weight of the girls is 40 kg. Find the average weight of the boys.

6.There are 120 students in a class in which 20 of them are girls and the rest are boys. If the average

   marks in Mathematics of the boys is 65% and that of girls is 80%, find the average marks of the

    class.

7.If the mean of n observations x1, x2, x3, .... x, is x, prove that the mean of the observations

   x1 + a, x2 + a, x3 + a, ... x, + a is x+a.

8.The percentage of marks obtained by students of a class in mathematics are 64, 36, 37, 23, 0, 19, 82,

    91, 72, 31, 10, 5. Find the median.

10.  Arun scored 36 marks in English, 44 marks in Hindi, 75 marks in Mathematics and x marks

      Science. If he has scored an average of 50 marks, find the value of x.

11.  Determine the median of 24, 23, a, a- 1, 12, 16, where a is the mean of 10, 20, 30, 40, 50.

12.  Find median and mode of the following data:

      6, 9, 12, 15, 9, 3, 6, 9, 12, 6, 12, 6, 10, 3, 6, 15, 6.

13. Following table shows the weights of 20 students.

     Weight (in kg)                59         60         62       65         64

     Number of Students         5          4           6         3            2

    Draw the horizontal bar graph for this data and find the mean weight.

14.The ages (in years) of 8 students of class IX are as Under:

     14, 15, 16, 14, 15, 15, 16, 15. Find the modal age and mean age.

15. Form the cumulative frequency table of less than series from following data:

      Class interval           Frequency

       0-10                               3

      10-20                            12

      20-30                            36

     30-40                             76

     40-50                             97

    50-60                              85

    60-70                              39

    70-80                              12

   80-90                               12

  90-100                               6

16.In a city, the weekly observations made in a study on the cost of living index, are given in the

    following table. Draw a frequency polygon for the data (without constructing a histogram).

   Cost of living          Number of weeks

   140-150                           5

   150-160                         10

   160-170                         20

   170-180                          9

   180-190                          6

   190-200                          2

17. 20 years ago, when my parents got married, their average age was 23 years, now the average age of

      my family consisting of myself and my parents is 34 years. What is my present age?

18.The daily wages paid to five workers in a factory are 20, 40, 42, 45, 30. If the wage of each worker

      is increased by ₹5. What will be the new average wage?

19. The scores of two batsman 'A' and 'B' in 5 innings of a test series are as follows:

        A: 58, 59, 60, 65, 40

       B: 120, 80, 30, 65, 12.

      On the basis of their average scores, determine who, of the two, may be a better choice for the man

      of the series.

20. The arithmetic mean of 100 observation is 24. If 6 is added to each of the observations and then each

      of them is multiplied by 2.5. Find the new arithmetic mean.

21.Mean of 10 observations is 2.5. If one observation, namely 2.5, is deleted, determine the new mean.

22. Find the mode of the following data by (i) inspection method (ii) Grouping Method.

      Wages (in ₹)        Number of persons

       125                            3

       175                            8

       225                          21

       275                            6

      325                             4

     375                              2

23.There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the

     mess were increased by ₹42 per day while the average expenditure per head diminished by ₹1.

     What was the original expenditure of the mess?

24.If mean of 7 observations in ascending order 28, 32, x, x+2,x+5,43, 45 is 38. Find x and hence find

     median.

25. Find median and mode of following data:

      24, 17, 13, 24, 26, 20, 26, 30, 8, 41, 24

     If one 24 is replaced by 26 find new median and mode.

26. The median of the following observations arranged in ascending order is 24. Find x.

       14, 18, x + 2, x + 4, 30, 34.

      Using the values of x, find the mean of the above data.

27.The following observations have been arranged in ascending order 29, 32, 48, 50, x, x+2, 72, 78, 84,

      95. If the median of this data is 63, then find value of x.

28.  Draw a histogram for the given data:

      Class interval          Frequency

        25-29                          5

       30-34                        15

       35-39                        23

       40-44                         20

       45-49                         10 

      50-54                          7

29.Draw a histogram and a frequency polygon for the following data:

    Class interval         Frequency

      0-50                              12

     51-100                          18

     101-150                        27

     151-200                        20

    201-250                        17

    251-300                        06

30. Draw a cumulative frequency diagram.

    Score           Number of students

    20-30                20

    30-40                35

    40-50                40

    50-60                32

    60-70                24

   70-80                27

   80-90                18

   90-100              34

31. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million

    (ppm) of a certain city. The data obtained for 30 days is as follows:

    0.03   0.08   0.08    0.09    0.04     0.17    0.16   0.05     0.02  0.06    0.18    0.20     0.11    0.08   0.12       0.13    0.22    0.07    0.08    0.01   0.10    0.06    0.09   0.18   0.11    0.07    0.05     0.07     0.01    0.04

  (a) Make a grouped frequency distribution table for this data with class intervals as 0.00 - 0.04,

   0.04-0.08 and so on.

(b) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?