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प्रश्न
Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:
| Variate | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Frequency | 1 | 2 | 3 | 1 | 2 | 4 | 2 | 1 | 1 | 2 | 1 |
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उत्तर
| Variate | Frequency (f) | Cumulative frequency |
| 10 | 1 | 1 |
| 11 | 2 | 3 |
| 12 | 3 | 6 |
| 13 | 1 | 7 |
| 14 | 2 | 9 |
| 15 | 4 | 13 |
| 16 | 2 | 15 |
| 17 | 1 | 16 |
| 18 | 1 | 17 |
| 19 | 2 | 19 |
| 20 | 1 | 20 |
No. of terms = 20
Lower Quartile (Q1) = `"n"/4 = 20/4` = 5th term = 12
Upper Quartile (Q3) = `("n" xx 3)/4 = (20 xx 3)/4` = 15th term = 16
Interquartile range = Q3 - Q1 = 16- 12 = 4
Semi-Interquartile range = `(Q_3 - Q_1)/2 = (16-12)/2 = 2`
Hence, Lower quartile = 12, upper quartile = 16, interquartile range = 4, semi-interquartile range = 2
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संबंधित प्रश्न
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| No. of students | 4 | 12 | 16 | 8 |
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| Daily earnings (in Rs): | 450−500 | 500−550 | 550−600 | 600−650 | 650−700 |
| Numbers of stores: | 16 | 10 | 7 | 3 | 1 |
The following histogram shows the monthly wages (in Rs) of workers in a factory:
(i) In which wage-group the largest number of workers are being kept? What is their number?
(ii) What wages are the least number of workers getting? What is the number of such workers?
(iii) What is the total number of workers?
(iv) What is the factory size?
The following frequency distribution table shows marks obtained by 180 students in Mathematics examination.
| Marks | No. of students |
| 0 - 10 | 25 |
| 10 - 20 | x |
| 20 - 30 | 30 |
| 30 - 40 | 2x |
| 40 - 50 | 65 |
Find the value of x. Also draw a histogram representing the above information.
Construct a frequency polygon without using a histogram for the following frequency distribution :
| Class Mark | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
| Frequency | 4 | 20 | 40 | 45 | 30 | 25 | 5 |
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| House Rent (In ₹ per month) | 400-600 | 600-800 | 800-1000 | 1000-1200 |
| Number of families | 200 | 240 | 300 | 50 |
The time taken, in seconds, to solve a problem for each of 25 persons is as follows:
| 16 | 20 | 26 | 27 | 28 |
| 30 | 33 | 37 | 38 | 40 |
| 42 | 43 | 46 | 46 | 47 |
| 48 | 49 | 50 | 53 | 58 |
| 59 | 60 | 64 | 52 | 20 |
(i) Construct a frequency distribution for these data using a class interval of 10 seconds.
(ii) In a school the weekly pocket money of 50 students is as follow's:
| Weekly pocket money (₹) | No. of student |
| 40 - 50 | 2 |
| 59 - 60 | 8 |
| 60 - 70 | 12 |
| 70 - 80 | 14 |
| 80 - 90 | 8 |
| 90 - 100 | 6 |
Draw a histogram and a frequency polygon on the same graph. Find mode from the graph.
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 |
Draw a histogram to represent the following data:
| Pocket money in ₹ | No. of Students |
| 150 - 200 | 10 |
| 200 - 250 | 5 |
| 250 - 300 | 7 |
| 300 - 350 | 4 |
| 350 - 400 | 3 |
The marks obtained by 50 students in Mathematics are given below.
(i) Make a frequency distribution table taking a class size of 10 marks
(ii) Draw a histogram and a frequency polygon.
| 52 | 33 | 56 | 52 | 44 | 59 | 47 | 61 | 49 | 61 |
| 47 | 52 | 67 | 39 | 89 | 57 | 64 | 58 | 63 | 65 |
| 32 | 64 | 50 | 54 | 42 | 48 | 22 | 37 | 59 | 63 |
| 36 | 35 | 48 | 48 | 55 | 62 | 74 | 43 | 41 | 51 |
| 08 | 71 | 30 | 18 | 43 | 28 | 20 | 40 | 58 | 49 |
