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

Median class is the class where the cumulative frequency just exceeds (N/2), where N is the total number of data points.

N = 4 + 8 + 10 + 12 + 10 + 4 + 2 = 50 (the total number of data points)

So, N/2 = 50/2 = 25

Now, find the class where the cumulative frequency just exceeds 25:

Cumulative Frequency for each class:
- For the first class (10-20): 4
- For the first two classes (10-20 and 20-30): 4 + 8 = 12
- For the first three classes (10-20, 20-30, and 30-40): 12 + 10 = 22
- For the first four classes (10-20, 20-30, 30-40, and 40-50): 22 + 12 = 34
- For the first five classes (10-20, 20-30, 30-40, 40-50, and 50-60): 34 + 10 = 44

So, the median class is the class 40-50, and the lower boundary of this class is 40.

Median = Lower boundary of the median class + (N/2 - Cumulative frequency of the class / Frequency of the median class) * Width of the class*

Median = 40 + (25 - 22) / 12 * 10 = 40 + 3/12 * 10 = 40 + 2.5 = 42.5

Therefore, the median is 42.5.

*Step 2: Find the Mode*

The mode is the class with the highest frequency.

In this case, the class with the highest frequency is the class 40-50 with a frequency of 12.

So, the mode is 40-50.

To summarize:
- Median: 42.5
- Mode: 40-50