35

Here, we observe that 5 students have scored marks below 10, i.e it lies between class interval 0-10 and 9 students have scored marks below 20.
So, (9-5)=4 students lie in the class interval 10-20. Continuing in the same manner, we get the following frequency distribution table for given data.

Marks	Number of students (fi)	Class marks (xi)	\(=\frac { x_{ i }^{ u_{ i } }-45 }{ h } \)	fiui
0-10	5	5	-4	-20
10-20	9-5=4	15	-3	-12
20-30	17-9=8	25	-2	-16
30-40	29-17=12	35	-1	-12
40-50	45-29=16	45	0	0
50-60	60-45=15	55	1	15
60-70	70-60=10	65	2	20
70-80	78-70=8	75	3	24
80-90	83-78=5	85	4	20
90-100	85-83=2	95	5	10
Total	\(n=\sum { f_{ i } } =85\)			\(\sum { f_{ i }u_{ i } } =29\)

Here, assumed mean(a)=45 and class width (h)=10
By step deviation method,
Mean \(\left( \overline { x } \right) =a+\left\{ \frac { \sum { f_{ i }u_{ i } } }{ \sum { f_{ i } } } \right\} \times h\)
\(=45+\left\{ \frac { 29 }{ 85 } \right\} \times 10=45+\frac { 58 }{ 17 } \\ =45+3.41=48.41\)

109.92

14.48km/L No, the manufacturer is claiming mileage 1.52km/L more than the average mileage.

f₁=28, f₂=24