MHT CET · Maths · Statistics
For the set of 50 observation, the sum of their squares is 3050 , their arithmetic mean is 6 . Hence the standard deviation of these observations is
- A 5
- B 3
- C 4
- D 6
Answer & Solution
Correct Answer
(A) 5
Step-by-step Solution
Detailed explanation
We have \(\mathrm{n}=50, \Sigma \mathrm{x}_{\mathrm{i}}^2=3050, \overline{\mathrm{x}}=6\)
\(\begin{aligned}
& \text { S.D. }=\sqrt{\frac{1}{n} \Sigma x_i^2-(\bar{x})^2} \\
& =\sqrt{\frac{3050}{50}-(6)^2}=\sqrt{61-36}=\sqrt{25}=5
\end{aligned}\)
\(\begin{aligned}
& \text { S.D. }=\sqrt{\frac{1}{n} \Sigma x_i^2-(\bar{x})^2} \\
& =\sqrt{\frac{3050}{50}-(6)^2}=\sqrt{61-36}=\sqrt{25}=5
\end{aligned}\)
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
- If \(\bar{a}\) is perpendicular to \(\bar{b}\) and \(\bar{c},|\vec{a}|=2\), \(|\bar{b}|=3,|\bar{c}|=4\) and the angle between \(\bar{b}\) and \(\bar{c}\) is \(\frac{\pi}{3}\), then \(\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]=\)MHT CET 2024 Easy
- Let two non-collinear vectors \(\hat{a}\) and \(\hat{b}\) form an acute angle. A point \(\mathrm{P}\) moves, so that at any time \(t\) the position vector \(\overline{\mathrm{OP}}\), where \(\mathrm{O}\) is origin, is given by \(\hat{a} \sin t+\hat{b} \cos t\), when \(P\) is farthest from origin \(\mathrm{O}\), let \(\mathrm{M}\) be the length of \(\overline{\mathrm{OP}}\) and \(\hat{\mathrm{u}}\) be the unit vector along \(\overline{\mathrm{OP}}\), thenMHT CET 2023 Hard
- If \(\bar{a}, \bar{b}, \bar{c}\) are three coplanar vectors such that \(|\bar{a}|=1,|\bar{b}|=2\), \(\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}=8\), the angle between \(\overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) is \(45^{\circ}\), then \(|\bar{a} \times(\bar{b} \times \bar{c})|=\)MHT CET 2025 Medium
- \(\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}}\left[\frac{\tan x}{\tan x+\cot x}\right] d x=\)MHT CET 2020 Easy
- The length of the projection of the line segment joining the points \((5,-1,4)\) and \((4,-1,3)\) on the plane \(x+y+z=7\) isMHT CET 2024 Medium
- If \(\mathrm{x}\) is a random variable with p.m.f. as follows.
\(P(X=x)=\frac{5}{16}, x=0,1 =\frac{k x}{48}, x=2,\) \(\text { then } E(x)=\frac{1}{4}, x=3\)MHT CET 2021 Medium
More PYQs from MHT CET
- In a full wave rectifier circuit without filter, the output current isMHT CET 2022 Easy
- Which one of the following processes depends on gravity?MHT CET 2007 Easy
- Which of the following polymers is used to obtain hose pipes for transport of gasoline?MHT CET 2022 Easy
- A simple harmonic motion is represented by \(\alpha \frac{d^2 x}{d t^2}+\beta x=0\). Its period isMHT CET 2022 Hard
- The slope of tangent at \((x, y)\) to a curve passing through \(\left(1, \frac{\pi}{4}\right)\) is \(\frac{y}{x}-\cos ^2 \frac{y}{x}\), then the equation of curve isMHT CET 2024 Hard
- Which among the following statement is TRUE about isotones?MHT CET 2022 Easy