The following table shows the number of patients of different age group who were discharged from the hospital in a particular month:

| Age (in years) | Number of Patients Discharged |
|--------------

Question

The following table shows the number of patients of different age group who were discharged from the hospital in a particular month:

| Age (in years) | Number of Patients Discharged |
|----------------|-------------------------------|
| $5 - 15$ | $6$ |
| $15 - 25$ | $11$ |
| $25 - 35$ | $21$ |
| $35 - 45$ | $23$ |
| $45 - 55$ | $14$ |
| $55 - 65$ | $5$ |
| **Total** | **80** |

Find the 'mean' and the 'mode' of the above data.

Accepted Answer

Step 1: | Age (in years) | Number of patients ($f_i$) | Class Mark ($x_i$) | $f_i x_i$ |
|----------------|---------------------------|---------------------|------------|
| $5 - 15$ | $6$ | $10$ | $60$ |
| $15 - 25$ | $11$ | $20$ | $220$ |
| $25 - 35$ | $21$ | $30$ | $630$ |
| $35 - 45$ | $23$ | $40$ | $920$ |
| $45 - 55$ | $14$ | $50$ | $700$ |
| $55 - 65$ | $5$ | $60$ | $300$ |
| **Total** | $\sum f_i = 80$ | | $\sum f_i x_i = 2830$ |
Step 2: Mean $= \frac{\sum f_i x_i}{\sum f_i} = \frac{2830}{80} = 35.38$ years (approx.)
Step 3: Modal class is $35 - 45$ (highest frequency $= 23$).
Step 4: Mode $= l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} 	imes h = 35 + \frac{23 - 21}{2(23) - 21 - 14} 	imes 10$
$= 35 + \frac{20}{11} = \frac{405}{11}$ or $36.82$ years (approx.)

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Solution