JEE Main 2024 (Online) 27th January Morning Shift | Statistics Question 39 | Mathematics

Let $\mathrm{a}_1, \mathrm{a}_2, \ldots \mathrm{a}_{10}$ be 10 observations such that $\sum\limits_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50$ and $\sum\limits_{\forall \mathrm{k} < \mathrm{j}} \mathrm{a}_{\mathrm{k}} \cdot \mathrm{a}_{\mathrm{j}}=1100$. Then the standard deviation of $\mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{10}$ is equal to :

$\sqrt{115}$

$\sqrt{5}$

JEE Main 2023 (Online) 15th April Morning Shift

MCQ (Single Correct Answer)

-1

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is :

JEE Main 2023 (Online) 11th April Evening Shift

MCQ (Single Correct Answer)

-1

Let the mean of 6 observations $$1,2,4,5, \mathrm{x}$$ and $$\mathrm{y}$$ be 5 and their variance be 10 . Then their mean deviation about the mean is equal to :

$$\frac{10}{3}$$

$$\frac{8}{3}$$

$$\frac{7}{3}$$

JEE Main 2023 (Online) 11th April Morning Shift

MCQ (Single Correct Answer)

-1

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of $$\mathrm{A}$$ and adding 2 to each element of $$\mathrm{B}$$. Then the sum of the mean and variance of the elements of $$\mathrm{C}$$ is ___________.