The following table shows the ages of the patients admitted in a hospital during a year:
| Age (in year) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
| Number of patients | 6 | 11 | 19 | 23 | 14 | 7 |
Find the mean of the above data.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 36.125
For grouped data, every value in a class is taken as the class mark, the middle of the class, and the mean is \(\displaystyle\frac{\sum fx}{\sum f}\), where \(f\) is the number of patients in the class.
Class marks and products (\(x\) times \(f\)):
Class 5-15, mark 10: \(10\times6=60\)
Class 15-25, mark 20: \(20\times11=220\)
Class 25-35, mark 30: \(30\times19=570\)
Class 35-45, mark 40: \(40\times23=920\)
Class 45-55, mark 50: \(50\times14=700\)
Class 55-65, mark 60: \(60\times7=420\)
The mean:
Total number of patients: \(\sum f=6+11+19+23+14+7=80\)
Sum of the products: \(\sum fx=2890\)
Mean \(\displaystyle=\frac{2890}{80}=\) 36.125 years