Tag: statistics and probability

Questions Related to statistics and probability

Find the coefficient of range for the data $43,24,38,56,22,39,45$

range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

  1. $0124$

  2. $0.212$

  3. $0.236$

  4. $0.436$

Show answer
Correct Option: D
Explanation:
Given data is $43, 24, 38, 56, 2, 39,45$.
The largest value of data is $x _m=56$
The smallest value of data is $x _0=22$
Coefficient of data $=\dfrac{56-22}{56+22}=\dfrac{34}{78}=0.4359\approx 0.436$
Hence, option D is correct.

The weight in Kg of 13 students in a class are $42.5,47.5,48.6,50.5,49,46.2,49.8,45.8,43.2,48,44.7,46.9,42.4$.Find the coefficient of range.

range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

  1. $0.077$

  2. $0.213$

  3. $0.0803$

  4. $0.093$

Show answer
Correct Option: C
Explanation:

The largest value of data is $x _m=49.8$

The smallest value of data is $x _0=42.4$
Coefficient of data$=\dfrac{49.8-42.4}{49.8+42.4}=\dfrac{7.4}{92.2}=0.08026\approx 0.0803$

Find the coefficient of range for the given data
$59,46,30,23,27,40,52,35,29$

range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

  1. $0.46$

  2. $0.44$

  3. $0.56$

  4. $0.124$

Show answer
Correct Option: B
Explanation:
Given data is $59, 46, 30, 23, 27, 40, 52, 35, 29$.
The largest value of data is $x _m=59$
The smallest value of data is $x _0=23$
Coefficient of data $=\dfrac{59-23}{59+23}=\dfrac{36}{82}=0.49\approx 0.44$

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

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

  1. -7

  2. -4

  3. 7

  4. 1.75

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Correct Option: C

If $\sigma$ $f _i$ $x _i$  = 20 and $\sigma$ $f _i$ = 4, what is the mean of the data.

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

  1. $\dfrac{1}{5}$

  2. $80$

  3. $16$

  4. $5$

Show answer
Correct Option: A
Explanation:
$\sigma fixi=20$
and $\sigma fi=4$

Hence, Mean $=\dfrac{\sigma fi}{\sigma fixi}=\dfrac{4}{20}=\dfrac{1}{5}$

Hence Option $A$ is correct

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

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

  1. $15$

  2. $20$

  3. $30$

  4. $33$

Show answer
Correct Option: D
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$=\dfrac{1}{n} \sum\limits _{i=1}^n(x _{i}-\bar x)^2$
$\implies \dfrac{1}{10}((6-15)^2+(8-15)^2+(10-15)^2+(12-15)^2+(14-15)^{2}+(16-15)^2+(18-15)^2+(20-15)^2$
$+(22-15)^2+(24-15)^2$

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

$\implies \dfrac{330}{10}=33$

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

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

  1. $\displaystyle \sigma _{x}= h\sigma _{u}$

  2. $\displaystyle \sigma _{x}= h+\sigma _{u}$

  3. $\displaystyle \sigma _{u}= h\sigma _{x}$

  4. $\displaystyle \sigma _{u}= h+\sigma _{x}$

Show answer
Correct Option: A
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.
$\displaystyle \therefore \sigma _{u}=\frac{\sigma _{x}}{h}$
$\Rightarrow h\sigma _{u}=\sigma _{x}$

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.

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

  1. $\sqrt{12}$

  2. $4\sqrt{2}$

  3. $6\sqrt{2}$

  4. $9\sqrt{2}$

Show answer
Correct Option: C
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 $2\sqrt{2}\times 3=6\sqrt{2}$

If the standard deviation of $x _1, x _2, .., x _n$ is $3.5$, then the standard deviation of $-2x _1-3, -2x _2-3$,....., -2x_n-3$ is?

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

  1. $-7$

  2. $-4$

  3. $7$

  4. $1.75$

Show answer
Correct Option: A
Explanation:
The Standard Deviation of a set remains unchanged if each data is increased or decreased by a constant however changes similarly when data is multiplied or divided by a constant.
$\therefore $ The SD for the new data set will be $=-2\times 3.5=-7$

Consider the following statements.Which of these is/are correct?

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

  1. Mode can be computed from histogram

  2. Median is not independent of change of scale

  3. Variance is independent of change of origin and scale

  4. none of these

Show answer
Correct Option: A,B
Explanation:

If we change scale by using x + h then median increases by h.
so median is not independent of change of scale.
From histogram we can see highest frequency so made.
Hence, options 'A' and 'B' are correct.