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 marks scored by students in Mathematics in a certain Examination are given below:
| Marks Scored | Number of Students |
| 0 — 20 | 3 |
| 20 — 40 | 8 |
| 40 — 60 | 19 |
| 60 — 80 | 18 |
| 80 — 100 | 6 |
Draw histogram for the above data.
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.

Observe the following frequency polygon and write the answers of the questions below it.
- Which class has the maximum number of students?
- Write the classes having zero frequency.
- What is the class-mark of the class, having frequency of 50 students?
- Write the lower and upper class limits of the class whose class mark is 85.
- How many students are in the class 80-90?
The age groups and the number of persons in the age groups, who donated blood in blood donation camp is given below. Find the measures of central angles to show the information by a pie diagram.
| Age group (Years) | 20-25 | 25-30 | 30-35 | 35-40 |
| No of persons | 80 | 60 | 35 | 25 |
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 |
Construct histograms for following frequency distribution:
| Class Mark | 6 | 12 | 18 | 24 | 30 | 36 |
| Frequency | 8 | 12 | 15 | 18 | 25 | 7 |
Construct a frequency polygon without using a histogram for the following frequency distribution :
| Class Interval | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 |
| Frequency | 8 | 12 | 10 | 16 | 6 |
The graphical representation of ungrouped data is ________
Draw a histogram for the given frequency distribution
| Age | 41 − 45 | 46 − 50 | 51 − 55 | 56 − 60 | 61 − 65 | 66 − 70 | 71 − 75 |
| Frequency | 4 | 9 | 17 | 25 | 15 | 8 | 2 |
Histogram shows the number of people owning the different number of books. Answer the question based on it.

The number of people owning books less than 40 is ______.
