Download App

STATISTICS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSSTATISTICS1 Mark
MCQ
Choose the correct answer. Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is:
  • ✓
    s
  • B
    ks
  • C
    s + k
  • D
    $\frac{\text{s}}{\text{k}}$
✓

Answer

Correct option: A.
s
Given observations are a, b, c d and e.
$\text{Mean}=\text{m}=\frac{\text{a}+\text{b}+\text{c}+\text{d}+\text{e}}{5}$
$\sum\text{x}_\text{i}={\text{a}+\text{b}+\text{c}+\text{d}+\text{e}}={5}\text{m}$
Now, $\text{mean}=\frac{\text{a}+\text{k}+\text{b}+\text{k}+\text{c}+\text{k}+\text{d}+\text{k}+\text{e}+\text{k}}{5}$
$=\frac{(\text{a}+\text{b}+\text{c}+\text{d}+\text{e})+5\text{k}}{5}=\text{m}+\text{k}$
$\therefore\ \text{SD}=\sqrt{\frac{{\sum(\text{x}_\text{i}^2+\text{k}^2+2\text{k}\text{x}_\text{i})}}{\text{n}}-(\text{m}^2+\text{k}^2+2\text{mk})}$
$=\sqrt{\frac{\sum\text{x}_\text{i}^2}{\text{n}}-\text{m}^2+\frac{2\text{k}\sum\text{x}_\text{i}}{\text{n}}-2\text{mk}}$
$=\sqrt{\frac{\sum\text{x}_\text{i}^2}{\text{n}}-\text{m}^2+2\text{km}-2\text{mk}}$ $\Big[\because\ \frac{\sum\text{x}_\text{i}}{\text{n}}=\text{m}\Big]$
$=\sqrt{\frac{\sum\text{x}_\text{i}^2}{\text{n}}-\text{m}^2}$
$=\text{s}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from STATISTICS→STATISTICS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the plane 7x + 11y + 13z = 3003 meets the axes in A, B, C then the centroid of $\Delta\text{ABC}$ is:
→
$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $
→
Consider the regions for complex number $z$

$A:\frac{1}{{\log_2 \left| z \right|}} - \frac{1}{{\log_2 \left| z \right| - 1}} - 1 < 0$ and $\left( {B:\operatorname{Im} \left( z \right) = 0} \right).$ The range of values of $Re(z)$
lying in the region $A \cap B$  is

→
The remainder when $(2021)^{203}$ is divided by $7$ is
→
Locus of a point which moves such that sum of the squares of its distances from the sides of a square of side unity is $9$, is
→
Choose the correct answer. Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is.
[Hint: Possible numbers of choosing or not choosing 5 green dyes, 4 blue dyes and 3 red dyes are $2^5, 2^4$ and $2^3$, respectively.]
→
The equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6) respectively is
→
If the equation ${x^2} + \lambda x + \mu = 0$ has equal roots and one root of the equation ${x^2} + \lambda x - 12 = 0$ is $2$, then $(\lambda ,\mu )=$
→
If the third term of a $G.P.$ is $4$ then the product of its first $5$ terms is
→
Which one of the following is the domain of the relation R defined on the set N of natural numbers as R = {(m, n) : 2m + 3n = 30m, in}.
→