Question : Directions: Study the histogram of the marks (in mathematics) distribution of fifty students in class IX and answer the following question:
The average marks of the students are:
Option 1: $53.2$
Option 2: $45.5$
Option 3: $60.2$
Option 4: $55.5$
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Correct Answer: $53.2$
Solution :
Required Average $=\frac{\text{Total marks obtained by the students}}{{\text{Total number of students in the class}}}$
Take the mid value of each interval while taking the sum of all observations.
Required Average $= \frac{(7 \times 10) + (8 \times 30) + (18 \times 50) + (4 \times 70) + (13 \times 90)}{50} \\$
$= \frac{70 + 240 + 900 + 280+1170}{50}\\$
$= \frac{2660}{50} \\$
$= 53.2$
Hence, the correct answer is $53.2$.
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