Tag: range and mean deviation

Questions Related to range and mean deviation

Calculation of Decile for individual data:
Find the $D _4$ and from the following data.
$20,22,24,26,28,30,32,34,36$

median percentiles and quartiles range and mean deviation mode

  1. 28

  2. 26

  3. 30

  4. 24

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Correct Option: B

Find $D _2$ for the following data:

Marks 10 20 30 40 50 60
No of Students 5 6 4 5 10 9
median percentiles and quartiles range and mean deviation mode

  1. 50 marks

  2. 20 marks

  3. 30 marks

  4. 40 marks

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Correct Option: B

Calculation of Decile for individual data:
Find the $D _8$ and from the following data.
$20,22,24,26,28,30,32,34,36$

median percentiles and quartiles range and mean deviation mode

  1. $D _8$=34

  2. $D _8$=32

  3. $D _8$=36

  4. $D _8$=28

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Correct Option: A

Find $D _4$ for the following data.

Marks 0-10 10-20 20-30 30-40 40-50 50-60
No of Students 5 6 5 5 10 9
median percentiles and quartiles range and mean deviation mode

  1. $D _4=30$

  2. $D _4=20$

  3. $D _4=40$

  4. $D _4=10$

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Correct Option: A

For the following grouped frequency distribution find the mode:

Class: 3-6 6-9 9-12 12-15 15-18 18-21 21-24
Frequency: 2 5 10 23 21 12 3
median percentiles and quartiles range and mean deviation mode

  1. 13.9

  2. 14.7

  3. 15.1

  4. 14.6

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Correct Option: A

The measure of dispersion is

economics measures of dispersion coefficient of variance variance and standard deviation statistics and probability

  1. Mean deviation

  2. S.D.

  3. quartile deviation

  4. all of the above

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Correct Option: D
Explanation:

Measures of dispersion include:
1)Sample standard deviation
2)Interquartile range (IQR) or Interdecile range
3)Range
4)Mean difference
5)Median absolute deviation (MAD)
6)Average absolute deviation (or simply called average deviation)
7)Distance standard deviation

The measure of dispersion is

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

  1. M.D.

  2. S.D.

  3. Q.D.

  4. All of these

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Correct Option: D
Explanation:

Mean deviation, standard deviation as well as quartile deviation is the measure of dispersion.
Hence, all of these are measure of dispersion.
(It is well known fact)


Which one is correct?
Statement 1:Positional measure of dispersion describes about the position that a particular data value has within a data set.
Statement 2:Quartiles and percentiles are positional measure of dispersion.

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

  1. $1$ only

  2. $2$ only

  3. $1$ and $2$ both

  4. Neither $1$ nor $2$

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Correct Option: C
Explanation:

Statement 1: is correct because positional measure of dispersion describes about the position that a particular data value has within a data set.
Statement 2:is correct because quartiles and percentiles are positional measure of dispersion.

If $\sum\limits _{i = 1}^9 {\left( {{x _i} - 5} \right) = 9}$ and $\sum\limits _{i = 1}^9 {{{\left( {{x _i} - 5} \right)}^2}}  = 45$, then the standard deviation of the $9$ items ${x _1},{x _2},.....,{x _9}$ is

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

  1. $2$

  2. $3$

  3. $9$

  4. $4$

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Correct Option: A
Explanation:
S.D of $xi-5$ is

$\sigma =\sqrt{\dfrac{\sum _{i=1}^{9}(xi-5)^2}{9}-\left [ \dfrac{\sum _{i=1}^{9}(xi-5)^2}{9} \right ]^2}$

$\sigma =\sqrt{5-1}=2$

What are the advantages of squaring a difference for calculating variance and standard deviation?

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

  1. Squaring makes each term positive so that values above the mean do not cancel below the mean.

  2. Squaring adds more weight to the larger differences, and in many cases this extra weight is appropriate since points further from the mean may be more significant.

  3. It complicates the calculations

  4. All are incorrect

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Correct Option: A,B
Explanation:

Since,

$\sigma _x=\sqrt{\cfrac{\sum (x _i-\bar x)^2}{N}}$
So, we can say that opion $A$ and $B$ are correct.