Fundamentals of Mathematical Statistics (BCA) 1st Sem Previous Year Solved Question Paper 2022

The median class is the one where the cumulative frequency just exceeds half of the total number of students (60/2 = 30).  the median class is "30-40" because its cumulative frequency (5 + x + 20 + 15) exceeds 30.

Median = L + [(N/2 - CF) * w]

- L is the lower boundary of the median class (30).
- N is the total number of students (60).
- CF is the cumulative frequency of the class before the median class (5 + x + 20).
- w is the class width (which is 10 in this case because the class is "30-40").

Median = 30 + [(30 - (5 + x + 20)) * 10] = 28.5

Now, solve for x:

30 + [(30 - (5 + x + 20)) * 10] = 28.5

Simplify and solve for x:

30 + (30 - 5 - x - 20) * 10 = 28.5
30 + (5 - x) * 10 = 28.5

Now, continue solving for x:

(5 - x) * 10 = 28.5 - 30
(5 - x) * 10 = -1.5

Divide both sides by 10:

5 - x = -0.15

Now, isolate x:

x = 5 + 0.15
x = 5.15

So, the value of x is approximately 5.15.

Now, to find the value of y, we can use the cumulative frequency we calculated earlier:

5 + x + 20 + 15 + y + 5 = 60

Substitute the value of x:

5 + 5.15 + 20 + 15 + y + 5 = 60

Now, solve for y:

5 + 5.15 + 20 + 15 + y + 5 = 60
50.15 + y = 60

Subtract 50.15 from both sides:

y = 60 - 50.15
y ≈ 9.85

So, the value of y is approximately 9.85.