Question

3. Find the values of x and y if the mean of the following data is 53 and total
numbers of observations is 100.
Marks 0-20 20-40 40-60 60-80 80-100
No of 15
students
< please give answer ​

Answer 1

Solution :

$\underline{\bf{Given\::}}}}$

Mean of the following data is 53 & total numbers of observations is 100, according to the question we can draw data of marks & no. of student's.

$\underline{\bf{Explanation\::}}}}$

$\bigstar$Using formula of the mean :

$\boxed{\bf{Mean=a+\frac{\sum fi.ui}{\sum fi} \times h}}}}$

$\begin{tabular}{|c|c|c|c|c|} \cline{1-5} \multicolumn{5}{|c|}{DATA} \\ \cline{1-5} \bf Class-Interval & \bf Frequency, (f_i) & \bf x_i & \bf u_i = \bf \dfrac{x_i -a}{h} & \bf f_i .\bf u_i \\ \cline{1-5} 0-20 & 15 & 10 & -3 & -45 \\ 20-40 & x & 30 & -2 & -2x \\ 40 - 60 & 21 & 50 & -1 & -21 \\ 60-80 & y &\sf a= \boxed{\bf 70 }& 0 & 0 \\ 80-100 & 17 & 90 & 1 & 17 \\ \cline{1-5} \sf Total &\sf 100 & & & \sf -49-2x \\ \cline{1-5} \end{tabular}}$

$\underbrace{\sf{According\:to\:the\:question\::}}}$

$\longrightarrow\sf{53=70+\dfrac{-49-2x}{100} \times 20}\\\\\\\longrightarrow\sf{53-70 = \dfrac{-49 - 2x}{\cancel{100}} \times \cancel{20}}\\\\\\\longrightarrow\sf{-17 = \dfrac{-49 - 2x}{5} }\\\\\longrightarrow\sf{-17\times 5=-(49 + 2x)\:\: \underbrace{\bf{cross-multiplication}}}\\\\\longrightarrow\sf{\cancel{-}85=\cancel{-}49 + 2x}\\\\\longrightarrow\sf{85=49+2x}\\\\\longrightarrow\sf{2x=85-49}\\\\\longrightarrow\sf{2x=36}\\\\\longrightarrow\sf{x=\cancel{36/2}}$

$\longrightarrow\bf{x=18}$

Now;

Sum of all frequency & given total observations;

$\longrightarrow\sf{15+x+ 21 + y + 17=100}\\\\\longrightarrow\sf{15+18+ 21 + y + 17=100}\\\\\longrightarrow\sf{71+y=100}\\\\\longrightarrow\sf{y=100-71}\\\\\longrightarrow\bf{y = 29}$

Thus;

The values of x & y will be 18 & 29 .

Answer 2

Answer:

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