Question

Find the value of x and y in following distribution if it known that the mean of the distribution is 1.46

No. of students 0 1 2 3 4 5 Total

Frequency 46 x y 25 10 5 200

Answer 1

Answer:

$x = 76 \\ \\ y = 38$

Solution:

We know that Mean
$= \frac{sum \: of \: all \: observations}{total \: number \: of \: observation} \\ \\ = \frac{\Sigma xf}{\Sigma f}$
Since total observation = 200

$\begin{table}[] \begin{tabular}{|l|l|l|} \cline{1-3} \begin{tabular}[c]{@{}l@{}}Observation\\ (x)\end{tabular} & Freq. & x f \\ \cline{1-3} 0 & 46 & 0 \\ \cline{1-3} 1 & x & x \\ \cline{1-3} 2 & y & 2y \\ \cline{1-3} 3 & 25 & 75 \\ \cline{1-3} 4 & 10 & 40 \\ \cline{1-3} 5 & 5 & 25 \\ \cline{1-3} Total & 200 & x+2y+140 \\ \cline{1-3} \end{tabular} \end{table}$

$1.46 = \frac{x + 2y + 140}{200} \\ \\ x + 2y + 140 = 292 \\ \\ x + 2y = 152 \: \: \: \: \: eq1$
From frequency addition

$86 + x + y = 200 \\ \\ x + y = 114 \: \: \: eq2$
Subtract eq1 and eq2

$y = 38$
put value of y in any one eq to get the value of x

$x + 38 = 114 \\ \\ x = 114 - 38 \\ \\ x = 76$
Hope it helps you.

Answer 2

Answer:

X = 76 and Y = 38

Step-by-step explanation:

Mean = sum of all observations

________________________________

Total no . of observation

X

0

1

2

3

4

5

Y

x

46

y

25

10

5

_____

200

XY

x

2y

75

40

25

_________

x+2y+140

x+2y+140

_______ = 1.46

200

x+2y= 152 ----------- Eq 1

86+x+y = 200 ( from X )

x+y = 114 -------- Eq 2

Substitute Eq 1 and Eq 2

y = 38

Now ,

x+y = 114 ( from Eq 2 )

x + 38 = 114

x= 114-38

x= 76

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