Mathematics — Standard (041) — CBSE Class 10 board question

Cumulative Frequency Table:

| Height (cm) | Frequency (f) | Cumulative Frequency (cf) |
|---|---|---|
| 130–135 | 4 | 4 |
| 135–140 | 11 | 15 |
| 140–145 | 12 | 27 |
| 145–150 | 7 | 34 |
| 150–155 | 10 | 44 |
| 155–160 | 6 | 50 |

Here, $n = 50$, so $\dfrac{n}{2} = 25$.

The cumulative frequency just greater than 25 is 27, which belongs to class 140–145.

∴ Median class = 140–145

$l = 140,\quad cf = 15,\quad f = 12,\quad h = 5$

$$\text{Median} = l + \left(\frac{\dfrac{n}{2} - cf}{f}\right) \times h = 140 + \left(\frac{25 - 15}{12}\right) \times 5$$

$$= 140 + \frac{50}{12} = 140 + 4.17 = \mathbf{144.17 \text{ cm}}$$

Source: Chapter 13, Section 13.4

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• Always build the cumulative frequency (cf) column first.
• Locate the median class: the class whose cf first exceeds $n/2$.
• Substitute carefully into the formula; examiners award marks for the table (1 mark), identifying the median class with correct values of $l, cf, f, h$ (1 mark), and the final calculation (1 mark).
• Round to 2 decimal places unless instructed otherwise.