Advertisements
Advertisements
Question
Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:
| Shoe size | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Frequency | 8 | 1 | 7 | 14 | 11 | 5 | 4 |
Advertisements
Solution
| Shoe size | Frequency (f) | Cumulative frequency |
| 5 | 8 | 8 |
| 6 | 1 | 9 |
| 7 | 7 | 16 |
| 8 | 14 | 30 |
| 9 | 11 | 41 |
| 10 | 5 | 46 |
| 11 | 4 | 50 |
No. of terms = 50
Lower Quartile (Q1) = `n/4 = 50/4` = 12.5th term = 7
Upper Quartile (Q3) = `(n xx 3)/4 = (50 xx 3)/4` = 37.5th term = 9
Interquartile range = Q3 - Q1 = 9-7 = 2
Semi-interquartile range = `(Q_3 - Q_1)/2 = (9-7)/2 = 1`
Hence, Lower quartile = 7, upper quartile = 9, interquartile range = 2, semi-interquartile range = 1
APPEARS IN
RELATED QUESTIONS
The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to:
- Frame a frequency distribution table.
- To calculate mean.
- To determine the Modal class.

Draw a histogram of the following data.
| Height of student (cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 |
| No. of students | 4 | 12 | 16 | 8 |
Draw a histogram to represent the following data:
| Monthly salary (in Rs) | Number of teachers |
| 5600−5700 | 8 |
| 5700−5800 | 4 |
| 5800−5900 | 3 |
| 5900−6000 | 5 |
| 6000−6100 | 2 |
| 6100−6200 | 3 |
| 6200−6300 | 1 |
| 6300−6400 | 2 |
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 |
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 a histogram for the following frequency distribution.
|
Use of electricity (Unit)
|
50 - 70 | 70 - 90 | 90 - 110 | 110 - 130 | 130 - 150 | 150 - 170 |
| No. of families | 150 | 400 | 460 | 540 | 600 | 350 |
Draw the Histogram and hence, the frequency polygon for the following frequency distribution:
| House Rent (In ₹ per month) | 400-600 | 600-800 | 800-1000 | 1000-1200 |
| Number of families | 200 | 240 | 300 | 50 |
Histogram is a graphical representation of ___________ data
Draw a histogram to represent the frequency distribution in question 91.
Draw a histogram for the following data.
| Class interval | 10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |
| Frequency | 30 | 98 | 80 | 58 | 29 | 50 |
