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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:
| Marks | 25 | 30 | 35 | 40 | 45 | 50 |
| No. of students | 6 | 15 | 12 | 10 | 18 | 9 |
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उत्तर
| Marks | No. of students (f) | Cumulative frequency |
| 25 | 6 | 6 |
| 30 | 15 | 21 |
| 35 | 12 | 33 |
| 40 | 10 | 43 |
| 45 | 18 | 61 |
| 50 | 9 | 70 |
No. of terms = 70
Lower Quartile (Q1) = `n/4 = 70/4` = 17.5th term = 30
Upper Quartile (Q3) = `(n xx 3)/4 = (70 xx 3)/4` = 52.5th term = 45
Interquartile range = Q3 - Q1 = 45-30 = 15
Semi-Interquartile range = `(Q_3 - Q_1)/2 = (45-30)/2 = 7.5`
Hence, Lower quartile = 30, upper quartile = 45, interquartile range = 15, semi -interquartile range = 7.5
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संबंधित प्रश्न
In the following table, the investment made by 210 families is shown. Present it in the form of a histogram.
|
Investment
(Thousand Rupees) |
10 - 15 | 15 - 20 | 20 - 25 | 25 - 30 | 30 - 35 |
| No. of families | 30 | 50 | 60 | 55 | 15 |
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 histograms for following frequency distribution:
| Class Interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Frequency | 8 | 20 | 34 | 22 | 10 | 6 |
Construct a frequency polygon without using a histogram for the following frequency distribution :
| Class Interval | 10-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 9 | 17 | 15 | 20 | 14 |
Draw the histogram for the following frequency distribution and hence estimate the mode for the distribution.
| Class | Frequency |
| 0 - 5 | 2 |
| 5 - 10 | 7 |
| 10 - 15 | 18 |
| 15 - 20 | 10 |
| 20 - 25 | 8 |
| 25 - 30 | 5 |
| Total | 24 |
The total area of the histogram is _________ to the total frequency of the given data
Draw a histogram and the frequency polygon in the same diagram to represent the following data
| Weight (in kg) | 50 − 55 | 56 − 61 | 62 − 67 | 68 − 73 | 74 − 79 | 80 − 85 | 86 − 91 |
| No. of persons | 15 | 8 | 12 | 17 | 9 | 10 | 6 |
Try yourself
- Next time when you watch your favourite TV programme, count the number of advertisements during each break. Use tally marks. Put a dot below the tally when you find children in any advertisement.
- Compare with your friends. Do you get different answers?
The height of a rectangle in a histogram shows the ______.
From the histogram given on the right, we can say that 1500 males above the age of 20 are literate.
