Tag: range and mean deviation

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

The coefficient of mean deviation from median of observations 40, 62, 54, 90, 68, 76 is

  1. 2.16

  2. 1.2

  3. 5

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arranging the given data in ascending order
40,54,62,68,76,90
Here, $n=6 (even)$
$M= \dfrac{\text{value of }3^{rd}\text{observation}+\text{value of }4^{th}\text{observation}}{2}$
Median $M=\dfrac{62+68}{2}=65$

Mean deviation about median $M.D=\dfrac{|40-65|+|54-65|+|62-65|+|68-65|+|76-65|+|90-65|}{65}$

$=\dfrac{25+11+3+3+11+25}{65}=1.2$

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

The difference between the maximum and the minimum observations in the data is

  1. class interval

  2. frequency

  3. cumulative frequency

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

The difference between maximum and the minimum observation in the data is range.

For example, suppose an experiment involves finding out the weight of lab rats and the values in grams are 320, 367, 423, 471 and 480. In this case, the range is simply computed as 480-320 = 160 grams.

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

The coefficient of range of a set of data is given to be $\dfrac18$. Then the ratio of the maximum value in the data to the minimum value is:

  1. $\dfrac81$
  2. $\dfrac98$
  3. $\dfrac97$
  4. $\dfrac87$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Coefficient of range of a set of data is given by $\dfrac{max-min}{max+min}$
$\dfrac{max-min}{max+min}=\dfrac{1}{8}$
$8max-8min=max+min$
$7max=9min$
$\dfrac{max}{min}=\dfrac{9}{7}$

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

The following are the wages of 8 workers in a factory. Find the range and coefficient of range. Wages are in dollars: 1400, 1450, 1520, 1380, 1485, 1495, 1575, 1440.

  1. $0.0231$
  2. $0.03112$
  3. $0.66$
  4. $0.02314$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The largest value of data is $x _m=1575$

The smallest value of data is $x _0=1380$
Range$=x _m-x _0=1575-1380=195$

Coefficient of data$=\dfrac{1575-1380}{1575+1380}=\dfrac{195}{2955}=0.0659\approx 0.66$

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

If the coefficient of range is $0.18$ and the largest value is $7.44$,then the smallest value is?

  1. $3.23$
  2. $4.15$
  3. $5.17$
  4. $5.14$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Coefficient of range$=\dfrac{x _m-x _0}{x _m+x _0}=\dfrac{7.44-x _0}{7.44+x _0}$

$0.18(7.44+x _0)=7.44-x _0$
$1.18x _0=7.44-7.44\times 0.18$
$1.18x _0=6.1008$
$x _0=5.17016\approx 5.17$

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

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

  1. $0124$
  2. $0.212$
  3. $0.236$
  4. $0.436$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.
Multiple choice range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

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.

  1. $0.077$
  2. $0.213$
  3. $0.0803$
  4. $0.093$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

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

  1. $0.46$
  2. $0.44$
  3. $0.56$
  4. $0.124$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $=\dfrac{59-23}{59+23}=\dfrac{36}{82}=0.49\approx 0.44$
Multiple choice business economics and quantitative methods measures of dispersion and skewness shortcut method for calculating mean deviation about mean mean deviation about mean and median range and mean deviation

When all the observations are same, the relation between A.M., G.M and H.M is _________.

  1. A.M. = G.M. = H.M.

  2. A.M. = G.M. > H.M.

  3. A.M. > G.M. > H.M.

  4. A.M. < G.M. < H.M.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When all observations in a dataset are identical, the Arithmetic Mean (AM), Geometric Mean (GM), and Harmonic Mean (HM) are all equal to that constant value.