JEE Mains · Maths · STD 11 - 13. statistics
If the data \(x_1, x_2, ...., x_{10}\) is such that the mean of first four of these is \(11\), the mean of the remaining six is \(16\) and the sum of squares of all of these is \(2,000\); then the standard deviation of this data is
- A \(2\sqrt 2 \)
- B \(2\)
- C \(4\)
- D \(\sqrt 2 \)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\({x_1} + ... + {x_4} = 44\) \({x_5} + ... + {x_{10}} = 96\) \(\bar x = 14,\sum {{x_i} = 140} \) Variance \( = \frac{{\sum {x_i^2} }}{n} - {{\bar x}^2} = 4\) Standard deviation \(=2\)
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 circle touching the \(x-\) axis at \((3, 0)\) and making an intercept of length \(8\) on the \(y-\) axis passes through the pointJEE Mains 2019 Hard
- If the function \( f(x) = \frac{e^{x}(e^{\tan x-x}-1)+\log_{e}(\sec x+\tan x)-x}{\tan x-x} \) is continuous at \( x=0 \), then the value of \( f(0) \) is equal toJEE Mains 2026 Hard
- If \(\int \operatorname{cosec}^5 x d x=\alpha \cot x \operatorname{cosec} x\left(\operatorname{cosec}^2 x+\frac{3}{2}\right)+\beta \log _e\left|\tan \frac{x}{2}\right|+C\) where \(\alpha, \beta \in \mathbb{R}\) and \(\mathrm{C}\) is constant of integration , then the value of \(8(\alpha+\beta)\) equals ...........JEE Mains 2024 Hard
- The range of \(f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)\) isJEE Mains 2023 Medium
- The minimum value of the function \(f(x)=\int \limits_0^2 e^{|x-t|} d t\) isJEE Mains 2023 Hard
- Let M and m respectively be the maximum and the minimum values of
\(f(x)=\left|\begin{array}{ccc}
1+\sin ^2 x & \cos ^2 x & 4 \sin 4 x \\
\sin ^2 x & 1+\cos ^2 x & 4 \sin 4 x \\
\sin ^2 x & \cos ^2 x & 1+4 \sin 4 x
\end{array}\right|, x \in \mathrm{R}\)
Then \(M^4-m^4\) is equal to :JEE Mains 2025 Medium
More PYQs from JEE Mains
- Let \(ABC\) be a triangle such that \(\overrightarrow{ BC }=\overrightarrow{ a }, \overrightarrow{ CA }=\overrightarrow{ b }\), \(\overrightarrow{ AB }=\overrightarrow{ c },|\overrightarrow{ a }|=6 \sqrt{2}, \quad|\overrightarrow{ b }|=2 \sqrt{3}\) and \(\overrightarrow{ b } \cdot \overrightarrow{ c }=12\) Consider the statements. \(( S 1):|(\overrightarrow{ a } \times \overrightarrow{ b })+(\overrightarrow{ c } \times \overrightarrow{ b })|-|\overrightarrow{ c }|=6(2 \sqrt{2}-1)\) \(( S 2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\). ThenJEE Mains 2022 Hard
- Let \(10\) vertical poles standing at equal distances on a straight line, subtend the same angle of elevation at a point \(O\) on this line and all the poles are on the same side of \(O\). If the height of the longest pole is \('h'\) and the distance of the foot of the smallest pole from \(O\) is \('a'\); then the distance between two consecutive poles, isJEE Mains 2015 Hard
- The area of the region in the first quadrant inside the circle \(x^2+y^2=8\) and outside the parabola \(\mathrm{y}^2=2 \mathrm{x}\) is equal to :JEE Mains 2024 Hard
- A straight line \(L\) through the point \((3, - 2)\) is inclined at an angle of \(60^o\) to the line \(\sqrt 3 x + y = 1\) . If \(L\) also intersects the \(x-\) axis, then the equation of \(L\) isJEE Mains 2015 Hard
- If \(a=\lim _{n \rightarrow \infty} \sum_{k=1}^{n} \frac{2 n}{n^{2}+k^{2}}\) and \(f(x)=\) \(\sqrt{\frac{1-\cos x}{1+\cos x}}, x \in(0,1)\), then.JEE Mains 2022 Hard
- From a lot of \(10\) items, which include \(3\) defective items, a sample of \(5\) items is drawn at random. Let the random variable \(\mathrm{X}\) denote the number of defective items in the sample. If the variance of \(X\) is \(\sigma^2\), then \(96 \sigma^2\) is equal to ....................JEE Mains 2024 Hard