Question:
In a class there are $n$ students. The mean of marks obtained by these $n$ students in an exam is 65. If the mark of one student is increased from 50 to 75 and the new mean is 66, then the value of $n$ is equal to
In a class there are $n$ students. The mean of marks obtained by these $n$ students in an exam is 65. If the mark of one student is increased from 50 to 75 and the new mean is 66, then the value of $n$ is equal to
Show Hint
If one data point changes by $\Delta$, the new mean $= \text{old mean} + \dfrac{\Delta}{n}$. Here $\Delta = 25$ and new mean $-$ old mean $= 1$, giving $n = 25$ directly.
Updated On: Apr 25, 2026
- 10
- 15
- 20
- 25
- 30
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Concept:
• Use the definition of mean: \[ \text{Mean} = \frac{\text{Sum of observations}}{n} \]
• When one value changes, the total sum changes accordingly.
Step 2: Detailed Explanation:
• Original sum: \[ 65n \]
• After increasing one mark from 50 to 75: \[ \text{New sum} = 65n + 25 \]
• New mean: \[ \frac{65n + 25}{n} = 66 \]
• Solving: \[ 65n + 25 = 66n \Rightarrow n = 25 \]
Step 3: Final Answer:
• \[ n = 25 \]
• Use the definition of mean: \[ \text{Mean} = \frac{\text{Sum of observations}}{n} \]
• When one value changes, the total sum changes accordingly.
Step 2: Detailed Explanation:
• Original sum: \[ 65n \]
• After increasing one mark from 50 to 75: \[ \text{New sum} = 65n + 25 \]
• New mean: \[ \frac{65n + 25}{n} = 66 \]
• Solving: \[ 65n + 25 = 66n \Rightarrow n = 25 \]
Step 3: Final Answer:
• \[ n = 25 \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Statistics Questions
- If the mean of six numbers is $41$, then the sum of these numbers is
- If the combined mean of two groups is $\frac{40}{3}$ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is equal to
- The $A$.$M$. of $9$ terms is $15$. If one more term is added to this series, then the $A$.$M$. becomes $16$. The value of the added term is
- If the mean of the numbers $a, b, 8,5,10$ is $6$ and their variance is $6.8$, then $ab$ is equal to
- If $\displaystyle\sum^{9}_{i-1}\left(x_{i}-5\right)=9$ and $\displaystyle\sum^{9}_{i-1}\left(x_{i}-5\right)^{2}=45$ , then the standard deviation of the $9$ items $x_{1}, x_{2} ,\cdots, x_{9}$ is
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions