Statistics

12. The following table lists the frequency distribution of 40 observations. The mean of the data is 29. What are the respective values of f1 and f2?

           Class interval     0 – 10     10 – 20     20 – 30     30 – 40     40 – 50     50 – 60

            Frequency (fi)        8               7              f1              8                8                f2

13. In a college, the marks of students are given out of 1000. The given data shows marksobtained by students in a course. What is the median of the given data?

 

Marks obtained	Number of students
More than 100	60
More than 200	55
More than 300	43
More than 400	36
More than 500	32
More than 600	30
More than 700	17
More than 800	8
More than 900	3

14. The number of students absent in a school was recorded every day for about 80 days and the median was found to be 46. Due to mishandling, some data was lost. The available data was written in the form of the table below. The missing observations x1 and x2 are

Days        10-20     20-30    30-40    40-50    50-60    60-70    70-80        Total

No. of absentees    12          30          x1          65         x2           25         18            229

15. Some data is given below. If the mode of the data is 84, then what is the value of x?

Class Interval	Frequency
0 − 20	3
20 − 40	9
40 − 60	12
60 − 80	12
80 − 100	x
100 − 120	6
120 − 140	5
140 − 160	12
160 − 180	5
180 − 200	7

16. The following table represents the ranges of annual incomes of 75 families in a particular locality. What is the annual income of most of the families?

 

Annual income(in Rs)	Number of families
100000 – 200000	8
200000 – 300000	9
300000 – 400000	17
400000 – 500000	18
500000 – 600000	14
600000 – 700000	6
700000 – 800000	3

17. The constituents of a chemical mixture had been classified according to their weights. The constituents were heated and kept aside for a couple of weeks. The median weight in the first weighing was recorded as 20.83 gm while in the second weighing it was 17.35 gm. It was later found that some frequencies a and b in the first weighing and x and y in the second were missing. It was known that 3a = x and 2b = y. The respective values of a and b are

Class	1st weighing
0-5	a	x
5-10	b	y
10-15	11	40
15-20	52	50
20-25	75	30
25-30	22	28

18. The following table shows the frequency distributions of 80 observations. Which of the following ogives correctly represents the “more than” ogive for the given data?

                                               
                                                 (A)                                                       (B)

 

 

19. Marks             Number of students Less than of   More than of

              0 – 10                        4                              4                         59
            10 − 20                        8                             12                       55
            20 − 30                       11                            23                       47
            30 − 40                       15                            38                       36
            40 − 50                       12                            50                       21
            50 − 60                        6                             56                        9
            60 − 70                        3                             59                        3

Draw a ‘more than’ ogive curve & a ‘less than’ ogive curve of the above data.

20. The following distribution gives the daily income of 50 workers of a factory.

 

Daily income (in Rs)	100 − 120	120 − 140	140 − 160	160 − 180	180 − 200
Number of workers	12	14	8	6	10

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

21. During the medical check-up of 35 students of a class, their weights were recorded as follows:

 

Weight (in kg)	Number of students
Less than 38	0
Less than 40	3
Less than 42	5
Less than 44	9
Less than 46	14
Less than 48	28
Less than 50	32
Less than 52	35

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula.

22. The following table gives production yield per hectare of wheat of 100 farms of a village.

       

Production yield (in kg/ha)	50 − 55	55 − 60	60 − 65	65 − 70	70 − 75	75 − 80
Number of farms	2	8	12	24	38	16

 

Change the distribution to a more than type distribution and draw ogive.

23. The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

 

Length (in mm)	Number or leaves fi
118 − 126	3
127 − 135	5
136 − 144	9
145 − 153	12
154 − 162	5
163 − 171	4
172 − 180	2

Find the median length of the leaves.
(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 − 126.5, 126.5 − 135.5… 171.5 − 180.5)

24. If the median of the distribution is given below is 28.5, find the values of x and y.

Class interval	Frequency
0 − 10	5
10 − 20	x
20 − 30	20
30 − 40	15
40 − 50	y
50 − 60	5
Total	60

25. In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes	50 − 52	53 − 55	56 − 58	59 − 61	62 − 64
Number of boxes	15	110	135	115	25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Prepared By:
Mr. Vijay Chawla
Email [email protected]
9899114400