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Multiple choice maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

Let $D$ represent a repeating decimal. If $P$ denotes the $r$ figures of $D$ which do not repeat themselves, and $Q$ denotes the $s$ figures which do repeat themselves, then the incorrect expression is

  1. $D = P.QQQ....$
  2. $10^{r}D = P.QQQ...$
  3. $10^{r + s}D = PQ .QQQ .....$
  4. $10^{r}(10^{s} - 1)D = Q(P - 1)$
  5. $10^{r} . 10^{2s}D = PQ.QQQ...$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$D = .PQQQ .... = .a _{1} ...a _{r}b _{1} ...b _{x}b _{1} ...b _{s} ...$ So $(a), (b), (c)$ and $(e)$ are all correct choices. To check that $(d)$ is incorrect, we have
$10^{r + s}D - 10^{r}D = PQ - P. \therefore 10^{r}(10^{s} - 1)D = P(Q - 1)$.

Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

If the standard deviation of $x _{1},x _{2},.....x _{n}$ is 3.5, then the standard deviatiuon of $-2x _{1}-3,-2x _{2}-3....,-2x _{n}-3$ is

  1. -7

  2. -4

  3. 7

  4. 1.75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Standard deviation is independent of the change of origin (adding or subtracting a constant) and is scaled by the absolute value of the change of scale (multiplying by a constant). If the original SD is 3.5, the new SD is | -2 | * 3.5 = 7.

Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

The variance of the data $6,\ 8,\ 10,\ 12\,,14\,,\ 16,\ 18,\ 20,\ 22,\ 24$ is

  1. $15$
  2. $20$
  3. $30$
  4. $33$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Mistake :$14$ is not given
Mean $\bar x=\dfrac{6+8+10+12+14+16+18+20+22+24}{10}=\dfrac{150}{10}=15$
Variance$=\dfrac{1}{n} \sum\limits _{i=1}^n(x _{i}-\bar x)^2$
$\implies \dfrac{1}{10}((6-15)^2+(8-15)^2+(10-15)^2+(12-15)^2+(14-15)^{2}+(16-15)^2+(18-15)^2+(20-15)^2$
$+(22-15)^2+(24-15)^2$

$\implies \dfrac{81+49+25+9+1+1+9+25+49+81}{10}$

$\implies \dfrac{330}{10}=33$
Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

The variate x and u are related by $\displaystyle u= \frac{x-a}{h}$ then correct relation between $\displaystyle \sigma _{x}:and:\sigma _{u}$

  1. $\displaystyle \sigma _{x}= h\sigma _{u}$
  2. $\displaystyle \sigma _{x}= h+\sigma _{u}$
  3. $\displaystyle \sigma _{u}= h\sigma _{x}$
  4. $\displaystyle \sigma _{u}= h+\sigma _{x}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given $\displaystyle u =\frac{x}{h}-\frac{a}{h}$
Since,S.D. is not depend on change of origin but it is depend on change of scale.
$\displaystyle \therefore \sigma _{u}=\frac{\sigma _{x}}{h}$
$\Rightarrow h\sigma _{u}=\sigma _{x}$

Multiple choice maths statistics and probability coefficient of variance variance and standard deviation measures of dispersion range and mean deviation

Standard deviation of a collection of data is $2\sqrt{2}$. If each value in a data set  is multipled by $3$, then the standard deviation of the new data is.

  1. $\sqrt{12}$
  2. $4\sqrt{2}$
  3. $6\sqrt{2}$
  4. $9\sqrt{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The standard deviation would also be multiplied by $3$.
Because the mean would also be $3x$ larger, the differences from the mean would be $3x$ larger too.
It is the same idea as if you were looking at your data set through an enlarging lens- everything would be $3x$ bigger, not only the data values, but also the mean, the differences from the mean, but just everything!
$\therefore$ the standard deviation becomes $2\sqrt{2}\times 3=6\sqrt{2}$