KCET · Maths · Statistics
The mean of 100 observations is 50 and their standard deviation is 5 . Then, the sum of squares of all observations is
- A \(252500\)
- B \(250000\)
- C \(255000\)
- D \(50000\)
Answer & Solution
Correct Answer
(A) \(252500\)
Step-by-step Solution
Detailed explanation
We know, standard deviation,
\(\begin{aligned} P^2 & =\frac{\Sigma x^2}{n}-(\bar{x})^2 \\ P & =5, \Sigma x=50, n=100\end{aligned}\)
\(\begin{aligned} & \Rightarrow \quad 25=\frac{\Sigma x^2}{100}-(50)^2 \\ & \Rightarrow \quad \Sigma x^2=252500\end{aligned}\)
Thus, sum of squares of all observation in 252500 .
\(\begin{aligned} P^2 & =\frac{\Sigma x^2}{n}-(\bar{x})^2 \\ P & =5, \Sigma x=50, n=100\end{aligned}\)
\(\begin{aligned} & \Rightarrow \quad 25=\frac{\Sigma x^2}{100}-(50)^2 \\ & \Rightarrow \quad \Sigma x^2=252500\end{aligned}\)
Thus, sum of squares of all observation in 252500 .
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- A vector perpendicular to the plane containing the points \(A(1,-1,2), B(2,0,-1), C(0,2,1)\) isKCET 2007 Medium
- The general solution of the differential equation \(x^{2} d y-2 x y d x=x^{4} \cos x d x\) isKCET 2020 Easy
- The value of \( \int_{-\pi / 4}^{\pi / 4} \sin ^{103} x \cdot \cos ^{101} x \mathrm{~d} \mathrm{x} \) isKCET 2016 Easy
- The sum of the degree and order of the differential equation \(\left(1+y_1^2\right)^{2 / 3}=y_2\) isKCET 2022 Easy
- The contrapositive of the converse of the statement "If \( x \) is a prime number then \( x \) is odd" isKCET 2016 Medium
- The order of differential equation of all circles of given radius ' \( a \) ' isKCET 2015 Medium
More PYQs from KCET
- The points \((11,9),(2,1)\) and \((2,-1)\) are the mid-points of the sides of the triangle. Then, the centroid isKCET 2012 Medium
- The volume of \(0.1 \mathrm{M}\) oxalic acid that can be completely oxidized by \(20 \mathrm{~mL}\) of \(0.025 \mathrm{M}\) \(\mathrm{KMnO}_{4}\) solution isKCET 2012 Medium
- Three resistances \( 2 \Omega, 3 \Omega \) and \( 4 \Omega \) are connected in parallel. The ratio of currents passing through them when a potential difference is applied across its ends will beKCET 2015 Easy
- If \( y=\tan ^{-1}\left(\frac{\sin x+\cos x}{\cos x-\sin x}\right) \), then \( \frac{d y}{d x} \) is equal toKCET 2017 Medium
- \(\mathrm{R}\) is a relation on \(\mathrm{N}\) given by \(R=\{(x, y): 4 x+3 y=20\}\). Which of the following belongs to \(R\) ?KCET 2008 Easy
- If \(A_n=\left[\begin{array}{cc}1-n & n \\ n & 1-n\end{array}\right]\), then \(\left|A_1\right|+\left|A_2\right|+\ldots\left|A_{2021}\right|=\)KCET 2022 Medium