Question
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.
Solution
The frequency distribution table of less than type is as follows
Daily income (in Rs) (upper class limits) |
Cumulative frequency |
Less than 120 | 12 |
Less than 140 | 12 + 14 = 26 |
Less than 160 | 26 + 8 = 34 |
Less than 180 | 34 + 6 = 40 |
Less than 200 | 40 + 10 = 50 |
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-axis, its ogive can be drawn as follows.
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Calculate the missing frequency form the following distribution, it being given that the median of the distribution is 24
Age (in years) | 0 – 10 | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 |
Number of persons |
5 | 25 | ? | 18 | 7 |
The following table, construct the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.
Marks obtained (in percent) | 11 – 20 | 21 – 30 | 31 – 40 | 41 – 50 | 51 – 60 | 61 – 70 | 71 – 80 |
Number of Students | 141 | 221 | 439 | 529 | 495 | 322 | 153 |
(a) Convert the given frequency distribution into the continuous form.
(b) Find the median class and write its class mark.
(c) Find the modal class and write its cumulative frequency.
The following table gives the life-time (in days) of 100 electric bulbs of a certain brand.
Life-tine (in days) | Less than 50 |
Less than 100 |
Less than 150 |
Less than 200 |
Less than 250 |
Less than 300 |
Number of Bulbs | 7 | 21 | 52 | 9 | 91 | 100 |
The following frequency distribution gives the monthly consumption of electricity ofr 64 consumers of locality.
Monthly consumption (in units) | 65 – 85 | 85 – 105 | 105 – 125 | 125 – 145 | 145 – 165 | 165 – 185 |
Number of consumers | 4 | 5 | 13 | 20 | 14 | 8 |
Form a ‘ more than type’ cumulative frequency distribution.
The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:
Age (in years) | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 -70 |
Number of patients | 6 | 42 | 55 | 70 | 53 | 20 |
Form a ‘less than type’ cumulative frequency distribution.