Short Answer TypeThe following table gives the distribution of the life-time of 400 new lamps.
|
Life-time (hrs.) |
No. of lamps |
|
1500-2000 |
14 |
|
2000-2500 |
56 |
|
2500-3000 |
60 |
|
3000-3500 |
86 |
|
3500-4000 |
74 |
|
4000-4500 |
62 |
|
4500-5000 |
48 |
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
|
Number of letters |
1-4 |
4-7 |
7-10 |
10-13 |
13-16 |
16-19 |
|
Number of surnames |
6 |
30 |
40 |
16 |
4 |
4 |
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
|
Number of letters |
Number of surnames |
Cumulative frequency |
|
1-4 |
6 |
6 |
|
4-7 |
30 |
36 |
|
7-10 |
40 |
76 |
|
10-13 |
16 |
92 |
|
13-16 |
4 |
96 |
|
16-19 |
4 |
100 |
|
x = 100 |
We have n = 100, so 
th observation = 50th observation.
So, median lies in the group of 7-10.
i.e. Median class = 7 - 10
Now, we have Median class = 70 - 10 l = 7, 
, cf = 36, f = 40 and h =3
Now, substituting these values in the formula of median, we get
Hence, the median number of letters in the surnames is 8.05.
The distribution below gives the weights of 30 students of a class. Find the Median weight of the students.
|
Weight (in k.g) |
40-45 |
45-50 |
50-55 |
55-60 |
60-65 |
65-70 |
70-75 |
|
No. of students (f) |
2 |
3 |
8 |
6 |
6 |
3 |
2 |
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.
Long Answer TypeDurine the medical check-up of 35 students of a class, their weight 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 |
During a less than type ogive for the given data. Hence obtain the median weight from the graph - and verify the result by using the formula.
Short Answer TypeThe 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 its ogive.
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