Calculate the mean of the distribution given below using the short-cut method- -4 MARKS-Wline Marks - No- of students IINhine 11-20 - 221-30 - 6 131-40 - 10 41-50 - 12 151-60 - 9 161-70 - 7 171-80 - 4 Whlinearray

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Standard X

Mathematics

Assumed Mean Method

Calculate the...

Question

Calculate the mean of the distribution given below using the short-cut method. [4 MARKS]
$\begin{matrix} M a r k s & N o . o f s t u d e n t s 11 - 20 & 2 21 - 30 & 6 31 - 40 & 10 41 - 50 & 12 51 - 60 & 9 61 - 70 & 7 71 - 80 & 4 \end{matrix}$

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Solution

Formula: 2 Marks
Solution: 2 Marks

We shall use short-cut method by taking assumed mean (A) = 45.5
$\begin{matrix} C l a s s e s & C l a s s & d_{i} = x_{i} - A & F r e q u e n c y & f_{i} d_{i} m a r k (x_{i}) & f_{i} 11 - 20 & 15.5 & - 30 & 2 & - 60 21 - 30 & 25.5 & - 20 & 6 & - 120 31 - 40 & 35.5 & - 10 & 10 & - 100 41 - 50 & 45.5 & 0 & 12 & 0 51 - 60 & 55.5 & 10 & 9 & 90 61 - 70 & 65.5 & 20 & 7 & 140 71 - 80 & 75.5 & 30 & 4 & 120 \end{matrix}$
Mean $= A + \frac{\sum f_{i} d_{i}}{\sum f_{i}} = 45.5 + \frac{70}{50}$
$= 45.5 + 1.4 = 46.9$

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Calculate the mean of the distribution given below using the short-cut method. [4 MARKS] MarksNo. of students11−20221−30631−401041−501251−60961−70771−804

Calculate the mean of the distribution given below using the short-cut method. [4 MARKS]
$\begin{matrix} M a r k s & N o . o f s t u d e n t s 11 - 20 & 2 21 - 30 & 6 31 - 40 & 10 41 - 50 & 12 51 - 60 & 9 61 - 70 & 7 71 - 80 & 4 \end{matrix}$