The marks out of 50 obtained by 100 students in a test are given below as:
|
Marks obtained |
20 |
25 |
28 |
29 |
33 |
38 |
42 |
43 |
|
Number of students |
6 |
20 |
24 |
28 |
15 |
4 |
2 |
1 |
Find the value of the (3 mode - 2 median).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30
Let’s solve step by step.
Step 1: Organize the data
|
Marks (x) |
Frequency (f) |
Cumulative frequency (CF) |
|
20 |
6 |
6 |
|
25 |
20 |
26 |
|
28 |
24 |
50 |
|
29 |
28 |
78 |
|
33 |
15 |
93 |
|
38 |
4 |
97 |
|
42 |
2 |
99 |
|
43 |
1 |
100 |
- Total students = 100
Step 2: Find the Median
- Median position = $\frac{N}{2} = \frac{100}{2} = 50^\text{th}$ value
The 50th value falls in the class 28–29 (cumulative frequency just reaching 50 at 28).
- Median ≈ 28.5 (since 28 and 29 are close and majority of students around this group)
Step 3: Find the Mode
- Mode = the value with the highest frequency
- Highest frequency = 28 → Marks = 29
So, Mode = 29
Step 4: Calculate (3 × Mode − 2 × Median)
$3 \times 29 - 2 \times 28.5 = 87 - 57 = 30$