Explanation:

Let’s lay out the numbers:

- Classes: 40-50, 50-60, 60-70, 70-80

- Frequencies: 4, 3, 1, 2 

- Total students: 4+3+1+2 = 10

- Median position: (N/2)th value = (10/2) = 5th value

Now, put those frequencies together:

- 1st to 4th student = in 40-50

- 5th to 7th student = in 50-60

So the median falls in the 50-60 class.

Let’s use the median formula for a grouped frequency (continuous series):

M = l + [(N/2 – F) / f] × h

l = 50 (lower limit of median class)

N = 10

F = cumulative frequency before median class = 4

f = frequency of median class = 3

h = class interval = 10

Plug in the values:

M = 50 + [(5 – 4)/3] × 10

M = 50 + [1/3] × 10

M = 50 + 10/3

M = 50 + 3.33

M = 53.33

Now, 3M = 3 × 53.33 = 160 (rounded off, but strictly, 159.99).

Check your options:

- Option 1: 53 1/3

- Option 2: 60

- Option 3: 160

- Option 4: 180

Option 3 is correct and matches our calculation.

Here's why:

- We found the median in the correct class.

- We used the right formula.

- Calculations check out.

- The other options don’t fit the math.

Anything off? The only "catch" is the rounding method; 160 is the closest to the true value. Let me know if you want the detailed decimal or more context!