Draw an ogive for the given frequency distribution:
| Class Interval | $5 - 10$ | $10 - 15$ | $15 - 20$ | $20 - 25$ | $25 - 30$ | $30 - 35$ |
|---|---|---|---|---|---|---|
| Frequency | $3$ | $4$ | $6$ | $9$ | $7$ | $1$ |
Hence find the lower quartile, upper quartile and the inter-quartile range.
| Class Interval | Frequency | Cumulative Frequency |
|---|---|---|
| $5 - 10$ | $3$ | $3$ |
| $10 - 15$ | $4$ | $7$ |
| $15 - 20$ | $6$ | $13$ |
| $20 - 25$ | $9$ | $22$ |
| $25 - 30$ | $7$ | $29$ |
| $30 - 35$ | $1$ | $30$ |
Lower quartile $= Q_1 = \left(\dfrac{N}{4}\right)^{th}$ term $= \left(\dfrac{30}{4}\right)^{th}$ term $= 7.5^{th}$ term $= 15.5$
Upper quartile $= Q_3 = \left(\dfrac{3N}{4}\right)^{th}$ term $= \left(\dfrac{3 \times 30}{4}\right)^{th}$ term $= 22.5^{th}$ term $= 25.5$
Inter-quartile range $= Q_3 - Q_1 = 25.5 - 15.5 = 10$