Tag: range and mean deviation

Questions Related to range and mean deviation

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

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

  1. 2.16

  2. 1.2

  3. 5

  4. none of these

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Correct Option: B
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 $M.D=\dfrac{|40-65|+|54-65|+|62-65|+|68-65|+|76-65|+|90-65|}{65}$

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

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

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

  1. class interval

  2. frequency

  3. cumulative frequency

  4. range

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Correct Option: D
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.

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:

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

  1. $\dfrac81$

  2. $\dfrac98$

  3. $\dfrac97$

  4. $\dfrac87$

Show answer
Correct Option: C
Explanation:

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

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.

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

  1. $0.0231$

  2. $0.03112$

  3. $0.66$

  4. $0.02314$

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Correct Option: C
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$=\dfrac{1575-1380}{1575+1380}=\dfrac{195}{2955}=0.0659\approx 0.66$

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

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

  1. $3.23$

  2. $4.15$

  3. $5.17$

  4. $5.14$

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Correct Option: C
Explanation:

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

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

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. $0.436$

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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. $0.093$

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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 $=\dfrac{59-23}{59+23}=\dfrac{36}{82}=0.49\approx 0.44$

The median of the following observations is
$10, 8, -9, -12, 15, 0, 23, -3, -2, 13, -24, 28, 35, 42$

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

  1. $4$

  2. $-2$

  3. $7$

  4. $-9.75$

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Correct Option: A

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

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

  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.

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Correct Option: A