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Age (in years) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 |
Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |
Answer :
The class 35-45 has the maximum frequency, therefore, this is the modal class.
Here l = 35 , h = 10 , f1 = 23 , f0 = 21 , f2 =14
Now, let us substitute these values in the formula
\(Mode \ = \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)
\(= \ 35 \ + \ \frac{23 \ - \ 21}{2 \ × \ 23 \ - \ 21 \ - \ 14} \ × \ 10 \)
\(= \ 35 \ + \ \frac{2}{46 \ - \ 21 \ - \ 14} \ × \ 10 \)
\(= \ 35 \ + \ \frac{2}{11} \ × \ 10 \)
\(= \ 35 \ + \ 1.8 \ = \ 36.8 \)
Now, to calculate the Mean,
Class Interval | Frequency ( \(f_i\) ) | 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 |
\( \sum f_i \ = \ 80 \) | \( \sum f_i x_i \ = \ 2830 \) |
\(\therefore \) The mean of the given data = 35.37 years