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Expenditure | Number of families |
1000-1500 | 24 |
1500-2000 | 40 |
2000-2500 | 33 |
2500-3000 | 28 |
3000-3500 | 30 |
3500-4000 | 22 |
4000-4500 | 16 |
4500-5000 | 7 |
Answer :
The class 1500 – 2000 has the maximum frequency. Therefore, it is the modal class.
Here l = 1500,
h = 500,
f1 =40 ,
f0 =24 and
f2 =33
Now, let us substitute these values in the formula
Mode \(= \ l \ + \ ( \frac{f_1 \ - \ f_0}{2f_1 \ - \ f_0 \ - \ f_2}) \ × \ h \)
\(= \ 1500 \ + \ ( \frac{40 \ - \ 24}{2 \ × \ 40 \ - \ 24 \ - \ 33}) \ × \ 500\)
\(= \ 1500 \ + \ \frac{40 \ -\ 24}{80 \ - \ 24 \ - \ 33} \ × \ 500 \)
\(= \ 1500 \ + \ \frac{16}{23} \ × \ 500 \)
\(= \ 1500 \ + \ 347.83 \ = \ 1847.83 \)
\(\therefore \) Modal monthly expenditure = Rs. 1847.83
Let the assumed mean be A = 2750 and h = 500.
Class Interval | \(f_i \) | \( x_i \) | \(d_i \ = \ x_i \ - \ A \) | \(u_i \ = \ \frac{d_i}{h} \) | \(f_i u_i \) |
1000-1500 | 24 | 1250 | -1500 | -3 | -72 |
1500-2000 | 40 | 1750 | -1000 | -2 | -80 |
2000-2500 | 33 | 2250 | -500 | -1 | -33 |
2500-3000 | 28 | 2750 | 0 | 0 | 0 |
3000-3500 | 30 | 3250 | 500 | 1 | 30 |
3500-4000 | 22 | 3750 | 1000 | 2 | 44 |
4000-4500 | 16 | 4250 | 1500 | 3 | 48 |
4500-5000 | 7 | 4750 | 2000 | 4 | 28 |
\( \sum f_i \ = \ 200 \) | \( \sum f_i u_i \ = \ -35 \) |