NIMCET 2020 — Mathematics PYQ

1. Analysis of Set A

• Data values: $2,3,7,1,3,2,3$ (Number of terms, $n=7$)

• Mean of A:

  $$\text{Mean}=\frac{\sum x}{n}=\frac{2+3+7+1+3+2+3}{7}=\frac{21}{7}=3$$

• Median of A: Arrange the values in ascending order: $1,2,2,3,3,3,7$.

  Since $n=7$ (odd), the median is the ${\left(\frac{7+1}{2}\right)}^{\text{th}}=4^{\text{th}}$ term:

  $$\text{Median}=3$$

• Mode of A: The value that appears most frequently. Here, $3$ appears three times.

  $$\text{Mode}=3$$

Observation for Set A: $\text{Mean}=\text{Median}=\text{Mode}=3$.

2. Analysis of Set B

• Data values: $7,5,9,12,5,3,8$ (Number of terms, $n=7$)

• Median of B: Arrange the values in ascending order: $3,5,5,7,8,9,12$.

  The median is the $4^{\text{th}}$ term:

  $$\text{Median}=7$$

3. Analysis of Set C

• Data values: $4,4,11,7,2,3,4$

• Mode of C: The value that appears most frequently. Here, $4$ appears three times.

  $$\text{Mode}=4$$

Evaluating the Options

• Option A: Mean of A ($3$) $=$ Mode of C ($4$). $⟹$ Incorrect

• Option B: Mean of C is equal to Median of B ($7$). Let's check Mean of C: $\frac{4+4+11+7+2+3+4}{7}=\frac{35}{7}=5\ne 7$. $⟹$ Incorrect

• Option C: Median of B ($7$) $=$ Mode of A ($3$). $⟹$ Incorrect

• Option D: Mean, Median and Mode of A are same ($3=3=3$). $⟹$ Correct

Conclusion

The correct statement is that the mean, median, and mode of set A are all equal to $3$.

Correct Answer: D