Question
Compute variance and standard deviation for the following data:
✓
Answer
$\begin{aligned} & \bar{x}=\frac{\sum f _{ i } x_i}{ N }=\frac{542}{60}=9.03 \\ & \operatorname{Var}( X )=\sigma_x{ }^2=\frac{\sum f _{ i } x_i{ }^2}{ N }-(\bar{x})^2\end{aligned}$
$=\frac{6836}{60 \text {}}-(9.03)^2$
$\begin{aligned} & =113.93-81.54 \\ & =32.39\end{aligned}$
S.D. $=\sigma_x=\sqrt{\operatorname{Var}(X)}=\sqrt{32.39}=5.69$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In a cricket team tournament 16 teams participated. A sum of ₹ 8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹ 275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?
The face cards are removed frm a full pack. out of the remaining 40 cards, 4 are drawn at random. what is the probability that 6they belong to different suits?
Calculate the coefficient of variation of the following data.
23, 27, 25, 28, 21, 14, 16, 12, 18, 16
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?
Find the points on the line x + y – 4 = 0 which are at a unit distance from the line 4JC + 3y = 10.
Determine whether the following function is differentiable at $x=3$ where,
$f(x)=x^2+2, \text { for } x \geq 3$
$=6 x-7, \text { for } x<3$
→$f(x)=x^2+2, \text { for } x \geq 3$
$=6 x-7, \text { for } x<3$
Solve the following quadratic equations:
→$x^2+3 i x+10=0$
Find the real numbers $x$ and $y$ such that $\frac{x}{1+2 i}+\frac{y}{3+2 i}=\frac{5+6 i}{-1+8 i}$
→Find the distance of the point (3, 5) from the line 2x + 3y = 14 measured parallel to a line having slope $\frac{1}{2}.$
→Find matrix $X$ such that $AX = B,$ where $A=\left[\begin{array}{cc}1 & -2 \\ -2 & 1\end{array}\right]$ and $B=\left[\begin{array}{c}-3 \\ -1\end{array}\right]$
→