Tag: range and mean deviation

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Questions Related to range and mean deviation

Multiple choice median percentiles and quartiles range and mean deviation mode

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

  1. 28

  2. 26

  3. 30

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For individual data, D_k = value at position k*(n+1)/10. For n=9, D_4 = value at 4*(10)/10 = 4th position. The 4th value in the sorted list 20, 22, 24, 26, 28, 30, 32, 34, 36 is 26.

Multiple choice median percentiles and quartiles range and mean deviation mode

Find $D _2$ for the following data:

Marks 10 20 30 40 50 60
No of Students 5 6 4 5 10 9

  1. 50 marks

  2. 20 marks

  3. 30 marks

  4. 40 marks
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total students = 5+6+4+5+10+9 = 39. D_2 position = 2*(39+1)/10 = 8th position. Cumulative frequencies: 5, 11, 15, 20, 30, 39. The 8th value falls in the 20 marks category.

Multiple choice median percentiles and quartiles range and mean deviation mode

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

  1. $D _8$=34
  2. $D _8$=32
  3. $D _8$=36
  4. $D _8$=28
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For n=9, D_8 = value at 8*(10)/10 = 8th position. The 8th value in the sorted list 20, 22, 24, 26, 28, 30, 32, 34, 36 is 34.

Multiple choice median percentiles and quartiles range and mean deviation mode

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
  1. $D _4=30$
  2. $D _4=20$
  3. $D _4=40$
  4. $D _4=10$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total frequency = 44. D_4 position = 4*(44)/10 = 17.6. Cumulative frequencies: 5, 11, 16, 21, 31, 40. The 17.6th value falls in the 30-40 class interval.

Multiple choice median percentiles and quartiles range and mean deviation mode

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

  1. 13.9

  2. 14.7

  3. 15.1

  4. 14.6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The modal class is 12-15 because it has the highest frequency (23). Applying the standard mode formula for grouped data with lower limit 12, frequency 23, preceding frequency 10, succeeding frequency 21, and class width 3 gives 14.6.

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

The measure of dispersion is

  1. Mean deviation

  2. S.D.

  3. quartile deviation

  4. all of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
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

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

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.

  1. $1$ only
  2. $2$ only
  3. $1$ and $2$ both
  4. Neither $1$ nor $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $2$
  2. $3$
  3. $9$
  4. $4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
S.D of $xi-5$ is

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

$\sigma =\sqrt{5-1}=2$
Multiple choice economics measures of dispersion coefficient of variance variance and standard deviation statistics and probability range and mean deviation

What are the advantages of squaring a difference for calculating variance and standard 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
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

Since,

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