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Mathematics

The following table shows the distribution of the marks obtained by 50 students in an aptitude test.

Marks obtainedNo. of students
156
1818
2112
248
274
302

Find the mean, the median and the mode of the distribution.

Statistics

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Answer

Marks obtained (x)No. of students (f)Cumulative frequencyfx
156690
181824324
211236252
24844192
27448108
3025060
Total501026

By formula,

Mean = ΣfxΣf=102650\dfrac{Σfx}{Σf} = \dfrac{1026}{50} = 20.52

From table,

n (no. of terms) = 50, which is even.

By formula,

Median = n2\dfrac{n}{2} th term

= 502\dfrac{50}{2} = 25th term.

From table,

Marks obtained from 25th to 36th student = 21.

∴ Median = 21.

Maximum students have scored 18 marks.

∴ Mode = 18.

Hence, mean = 20.52, median = 21 and mode = 18.

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