Question:
If the mean of the following data is \(12.5\), find the value of \(k\).
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Class interval} & 0\text{-}5 & 5\text{-}10 & 10\text{-}15 & 15\text{-}20 & 20\text{-}25 \\
\hline
\text{Frequency} & 2 & k & 6 & 4 & 1 \\
\hline
\end{array}
\]
If the mean of the following data is \(12.5\), find the value of \(k\).
\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class interval} & 0\text{-}5 & 5\text{-}10 & 10\text{-}15 & 15\text{-}20 & 20\text{-}25 \\ \hline \text{Frequency} & 2 & k & 6 & 4 & 1 \\ \hline \end{array} \]
\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class interval} & 0\text{-}5 & 5\text{-}10 & 10\text{-}15 & 15\text{-}20 & 20\text{-}25 \\ \hline \text{Frequency} & 2 & k & 6 & 4 & 1 \\ \hline \end{array} \]
Show Hint
For grouped data,
\[
\boxed{
\bar{x}
=
\frac{\sum fx}{\sum f}
}
\]
where \(x\) is the class mark of each interval.
Updated On: Jul 16, 2026
- \(1\)
- \(2\)
- \(3\)
- \(4\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Find the class marks.
\[
2.5,\;7.5,\;12.5,\;17.5,\;22.5
\]
Step 2: Compute \(\sum f\) and \(\sum fx\). \[ \sum f=2+k+6+4+1=13+k. \] Also, \[ \sum fx = 2(2.5)+k(7.5)+6(12.5)+4(17.5)+1(22.5) \] \[ =5+7.5k+75+70+22.5 \] \[ =172.5+7.5k. \]
Step 3: Use the mean formula. Given, \[ \frac{172.5+7.5k}{13+k}=12.5. \] Therefore, \[ 172.5+7.5k = 162.5+12.5k. \] \[ 10=5k. \] \[ k=2. \]
Step 4: Final conclusion. \[ \boxed{k=2} \] Hence, the correct option is \(\boxed{(B)}\).
Step 2: Compute \(\sum f\) and \(\sum fx\). \[ \sum f=2+k+6+4+1=13+k. \] Also, \[ \sum fx = 2(2.5)+k(7.5)+6(12.5)+4(17.5)+1(22.5) \] \[ =5+7.5k+75+70+22.5 \] \[ =172.5+7.5k. \]
Step 3: Use the mean formula. Given, \[ \frac{172.5+7.5k}{13+k}=12.5. \] Therefore, \[ 172.5+7.5k = 162.5+12.5k. \] \[ 10=5k. \] \[ k=2. \]
Step 4: Final conclusion. \[ \boxed{k=2} \] Hence, the correct option is \(\boxed{(B)}\).
Was this answer helpful?
0
0
Top TG ICET Mathematical Ability Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
View More Questions
Top TG ICET Statistics Questions
- The lines $3x-2y=-6$ and $x+y=3$ meet the $Y$-axis at the point $A$ and meet the $X$-axis at the points $B$ and $C$. Then the area of $\triangle ABC$ (in sq. units) is
- If the line $5y=7x$ divides the line segment joining the points $(3,5)$ and $(-5,2)$ in the ratio $m:n$ (where $\gcd(m,n)=1$), then the least value of $m^{2}+n^{2}$ is}
- If the angle between the lines $7x+3py+5=0$ and $3x-14py+11=0$ is $\frac{\pi}{2}$, then a value of $p$ is}
- If \(m\) and \(c\) denote the slope and the \(y\)-intercept of the line \(3x-5y-6=0\), then \((m,c)=\)
- If the equation of the line passing through the point \((-4,3)\) and having a slope \(\left(-\frac{2}{3}\right)\) is \(ax+by=c\), then \(a^2+b^2-c^2=\)
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions