Calculate the mean of the distribution given below using the short cut methodWheNo- of students - 2 - 6 - 10 - 12 - 9 - 7 - 4 Whline array -4 MARKS-

Shortcut method: 2 Marks Mean: 2 Marks Let A = 45.5 [ Marks amp; Number of amp; Mid value amp; d_i =x_i A amp; f_i d_i; ...

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Standard X

Mathematics

Assumed Mean Method of Finding Mean

Calculate the...

Question

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

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Solution

Let $A = 45.5$
$\begin{matrix} M a r k s & N u m b e r o f & M i d - v a l u e & d_{i} = x_{i} - A & f_{i} d_{i} s t u d e n t s (f_{i}) & (x_{i}) 11 - 20 & 2 & 15.5 & - 30 & - 60 21 - 30 & 6 & 25.5 & - 20 & - 120 31 - 40 & 10 & 35.5 & - 10 & - 100 41 - 50 & 12 & A = 45.5 & 0 & 0 51 - 60 & 9 & 55.5 & 10 & 90 61 - 70 & 7 & 65.5 & 20 & 140 71 - 80 & 4 & 75.5 & 30 & 120 T o t a l & \sum f_{i} = 50 & \sum f_{i} d_{i} = 70 \end{matrix}$
Mean $(¯ x) = A + \frac{\sum f_{i} d_{I}}{\sum f_{i}}$
$= 45.5 + \frac{70}{50} = 45.5 + 1.4 = 46.9$

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Calculate the mean of the distribution given below using the short cut method Marks11−2021−3031−4041−5051−6061−7071−80No. of students261012974

Let A=45.5 MarksNumber ofMid−valuedi=xi−Afidistudents(fi)(xi)11−20215.5−30−6021−30625.5−20−12031−401035.5−10−10041−5012A=45.50051−60955.5109061−70765.52014071−80475.530120Total∑fi=50∑fidi=70 Mean (¯x)=A+∑fidI∑fi =45.5+7050=45.5+1.4=46.9

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