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Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data MCQs for JEE

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Master Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data through exam-style multiple-choice questions. This page features 12+ JEE MCQs covering Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data, each with verified answers and clear explanations.

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Part of Statistics and Probability in JEE Main Mathematics.

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Q1MathsUnit 13: Statistics and Probability
In an experiment with 15 observations on x,x, then following results were available: ∑x2=2830,∑x=170\sum x^{2}=2830, \sum x=170 One observation that was 20 was found to be wrong and was replaced by the correct value 30.30 . Then the corrected variance is:
Q2MathsUnit 13: Statistics and Probability
Find variance for following data:  Class 0−10−20−3010203040\begin{array}{lllll}\text { Class } & 0- & 10- & 20- & 30 \\ & 10 & 20 & 30 & 40\end{array} frequency ey 6 8
Q3MathsUnit 13: Statistics and Probability
The variance of observations 112,116,120,125,132 is
Q4MathsUnit 13: Statistics and Probability
The variance of the data 6,8,10,12,14,16,18,20,22,24 is
Q5MathsUnit 13: Statistics and Probability
Variance remains unchanged by change of
Q6MathsUnit 13: Statistics and Probability
The ages (in years) of a family of 6 members are 1,5,12,15,38 and 40 The standard deviation is found to be 15.9 After 10 years the standard deviation is
Q7MathsUnit 13: Statistics and Probability
Which of the following are dimensionless
Q8MathsUnit 13: Statistics and Probability
Assertion If rxy\boldsymbol{r}_{\boldsymbol{x} \boldsymbol{y}} i.e. r(x,y)=0.25,σx=0.1,σy=\boldsymbol{r}(\boldsymbol{x}, \boldsymbol{y})=\mathbf{0 . 2 5}, \boldsymbol{\sigma}_{\boldsymbol{x}}=\mathbf{0 . 1}, \boldsymbol{\sigma}_{\boldsymbol{y}}= 4,4, then byx=10b_{y x}=10 Reason byx=rσyσx\boldsymbol{b}_{\boldsymbol{y} \boldsymbol{x}}=\boldsymbol{r} \frac{\boldsymbol{\sigma}_{\boldsymbol{y}}}{\boldsymbol{\sigma}_{\boldsymbol{x}}}

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