Heights of $50$ students of class X of a school are recorded and following data is obtained:

| Height (in cm) | $130$-$135$ | $135$-$140$ | $140$-$145$ | $145$-$150$ | $150$-$155$ | $155$-$160$ |
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Question

Heights of $50$ students of class X of a school are recorded and following data is obtained:

| Height (in cm) | $130$-$135$ | $135$-$140$ | $140$-$145$ | $145$-$150$ | $150$-$155$ | $155$-$160$ |
|----------------|-------------|-------------|-------------|-------------|-------------|-------------|
| Number of Students | $4$ | $11$ | $12$ | $7$ | $10$ | $6$ |

Find the median height of the students.

Accepted Answer

Step 1: | Class | $f$ | $cf$ |
|-------|-----|------|
| $130$-$135$ | $4$ | $4$ |
| $135$-$140$ | $11$ | $15$ |
| $140$-$145$ | $12$ | $27$ |
| $145$-$150$ | $7$ | $34$ |
| $150$-$155$ | $10$ | $44$ |
| $155$-$160$ | $6$ | $50$ |
Step 2: Median class is $140$-$145$ ($\frac{N}{2} = 25$, $cf = 15 < 25$)
Step 3: Median $= 140 + \frac{5}{12}(25 - 15) = 140 + \frac{50}{12}$
Step 4: $= 144.1$ (approx). Hence, Median height is $144.1$ cm.

Question

Solution