The following table shows the number of patients of different age groups 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.
| Age (in years) C.I. | No. of Patients Discharged (f) |
Mid value (x) |
f.x. |
| 5 − 15 | 6 | 10 | 60 |
| 15 − 25 | 11 | 20 | 220 |
| 25 − 35 | 21 → f0 | 30 | 630 |
| 35 − 45 | 23 → f1 | 40 | 920 |
| 45 − 55 | 14 → f2 | 50 | 700 |
| 55 − 65 | 5 | 60 | 350 |
| Total | `bb(sumf = 80)` | `bb(sumfx = 2830)` |
Mean = `(∑fx)/(∑f)`
= `2830/80`
= 35.38
So, the mean of the given data is 35.38.
Mode:
The maximum frequency is 23, and it corresponds to the 35 – 45 age group.
f1 = 23, f0 = 21, f2 = 14
l = 35, h = 10
Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`
= `35 + ((23 - 21)/(2 xx 23 - 21 - 14)) xx 10`
= `35 + (2/(46 - 35)) xx 10`
= `35 + 20/11`
= 35 + 1.82
= 36.82
Therefore, the mode of the given data is 36.82.
