The following table shows the ages of the patients admitted in a hospital during a year:

| Age (in years) | $5 - 15$ | $15 - 25$ | $25 - 35$ | $35 - 45$ | $45 - 55$ | $55 - 65$ |
|----------------|--

Question

The following table shows the ages of the patients admitted in a hospital during a year:

| Age (in years) | $5 - 15$ | $15 - 25$ | $25 - 35$ | $35 - 45$ | $45 - 55$ | $55 - 65$ |
|----------------|----------|-----------|-----------|-----------|-----------|----------|
| Number of patients | $6$ | $11$ | $21$ | $23$ | $14$ | $5$ |

Find the mode and mean of the data given above.

Accepted Answer

Step 1: | Age (in years) | No. of patients ($f_i$) | Mid point ($x_i$) | $f_i x_i$ |
|----------------|------------------------|--------------------|----------|
| $5 - 15$ | $6$ | $10$ | $60$ |
| $15 - 25$ | $11$ | $20$ | $220$ |
| $25 - 35$ | $21$ | $30$ | $630$ |
| $35 - 45$ | $23$ | $40$ | $920$ |
| $45 - 55$ | $14$ | $50$ | $700$ |
| $55 - 65$ | $5$ | $60$ | $300$ |
| **Total** | $80$ | | $2830$ |
Step 2: Mean $= \frac{2830}{80} = 35.375$
Step 3: Modal class $= 35 - 45$ ($f_1 = 23$, $f_0 = 21$, $f_2 = 14$, $l = 35$, $h = 10$)
Step 4: Mode $= l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} 	imes h = 35 + \frac{23 - 21}{2 	imes 23 - 21 - 14} 	imes 10 = 35 + \frac{2}{11} 	imes 10$
Step 5: $= 35 + 1.81 = 36.81$. Mode $= 36.81$ years, Mean $= 35.375$ years.

Question

Solution