The following table gives the marks scored by students in an exam.

$\begin{matrix} Marks & No. of students Above 0 & 80 Above 10 & 77 Above 20 & 72 Above 30 & 65 Above 40 & 55 Above 50 & 43 Above 60 & 23 Above 70 & 16 Above 80 & 10 Above 90 & 8 Above 100 & 0 \end{matrix}$

Find the mean for the following data using assumed mean method. [4 MARKS]

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Solution

Table: 2 Marks
Application: 2 Marks
Let the assumed mean be 45

$\begin{matrix} Class interval & x_{i} & f_{i} & d_{i} & f_{i} d_{i} 0 - 10 & 5 & 3 & - 40 & - 120 10 - 20 & 15 & 5 & - 30 & - 150 20 - 30 & 25 & 7 & - 20 & - 140 30 - 40 & 35 & 10 & - 10 & - 100 40 - 50 & 45 & 12 & 0 & 0 50 - 60 & 55 & 20 & 10 & 200 60 - 70 & 65 & 7 & 20 & 140 70 - 80 & 75 & 6 & 30 & 180 80 - 90 & 85 & 2 & 40 & 80 90 - 100 & 95 & 8 & 50 & 400 \end{matrix}$

$\sum f_{i} = 80$

$\sum f_{i} d_{i} = 490$

Mean
$= 45 + \frac{490}{80}$

$= 45 + 6.125$

$= 51.25$

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The following table gives the marks scored by students in an exam. MarksNo. of studentsAbove 080Above 1077Above 2072Above 3065Above 4055Above 5043Above 6023Above 7016 Above 8010Above 908Above 1000 Find the mean for the following data using assumed mean method. [4 MARKS]