Statistics Test

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Statistics Test - 37

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following Statement is false?

A
Range is rigidly defined.

B
Range can be calculated for open-ended intervals.

C
Range is not based on all the terms of a given data.

D
Range does not give a clear picture of variation in Data.

Solution

Example:
$$\bullet$$ The set "A" is the Domain,
$$\bullet$$ The set "B" is the Codomain,
$$\bullet$$ And the set of elements that get pointed to in B(the actual values produced by the function) are the Range, also called the Image.
And we have:
$$\bullet$$ Domain: $$\{1, 2, 3, 4\}$$
$$\bullet$$ Codomain: $$\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$
$$\bullet$$ Range: $$\{3, 5, 7, 9\}$$.
Question 2
1 / -0

What are the objectives of measure of dispersion?

A
Helpful in use of further statistical analysis as in regression, correlation etc.

B
Reliability of measure of central tendency

C
Control of variability

D
All of the above

Solution

Objectives of measure of dispersion:
(i)Reliability of measure of central tendency
(ii)Control of variability
(iii)Helpful in use of further statistical analysis as in regression, correlation etc
Question 3
1 / -0

Find the mean of the first five prime numbers.

A
3.3

B
7.8

C
5.6

D
12.1

Solution

First five prime numbers are $$2, 3, 5, 7$$ and $$11.$$
Number of observations $$=5$$
$$Mean=\dfrac{Sum\,of\,the\,numbers}{No.\,of\,observations}$$
$$=\dfrac{2+3+5+7+11}{5}$$
$$=\dfrac{28}{5}$$
$$=5.6$$
Question 4
1 / -0

Which of the following are measures of dispersion?

A
Standard Deviation,Median,Range

B
Standard Deviation,Mode,Range

C
Standard Deviation,Variance,Range

D
Mean,Mode,Median

Solution

Standard Deviation, Variance, and Range are measures of dispersion but the Mean, Mode, and Median are the measure of central tendency.
Question 5
1 / -0

Which of the following are measures of central tendency.

A
Percentile, Quartile, Median

B
Median,Mode, Percentile

C
Percentile, Quartile, Mode

D
Mean,Mode, Median

Solution

Mean, Mode, Median are the measures of central tendency. Thus the correct option is C.
Question 6
1 / -0

An Um contains $$4$$ white and $$3$$ red balls. $$X$$ is the no. of red balls. Find the Mean and Variance of $$X$$.

A
$$\dfrac {9}{7}, \dfrac {24}{49}$$

B
$$\dfrac {9}{7}, \dfrac {25}{48}$$

C
$$\dfrac {9}{8}, \dfrac {24}{49}$$

D
$$\dfrac {9}{8}, \dfrac {24}{48}$$

Solution

Let x be the no. of red balls in a random draw of three balls. As these are $$8$$ red balls, double value of x are $$0, 1, 2, 3$$
$$p(0)=\dfrac{^{3}C_o\times {^{4}C_3}}{^{7}C_3}=\dfrac{4\times 3\times 2}{7\times 6\times 5}=\dfrac{4}{35}$$
$$p(1)=\dfrac{^{3}C_1\times {^{4}C_2}}{^{7}C_3}=\dfrac{3\times 6\times 6}{7\times 6\times 5}=\dfrac{18}{35}$$
$$p(2)=\dfrac{^{3}C_2\times {^{4}C_1}}{^{7}C_3}=\dfrac{3\times 4\times 6}{7\times 6\times 5}=\dfrac{12}{35}$$
$$p(3)=\dfrac{^{3}C_3\times {^{4}C_3}}{^{7}C_3}=\dfrac{1\times 1\times 6}{7\times 6\times 5}=\dfrac{1}{35}$$
for calculation of mean of variance
x    p(x) xp(x)    $$x^2p(x)$$
$$0$$ $$4/35$$    $$0$$    $$0$$
$$1$$    $$18/35$$ $$18/35$$    $$18/35$$
$$2$$ $$12/35$$ $$24/35$$ $$40/35$$
$$3$$ $$1/35$$ $$3/35$$    $$9/35$$
Total    $$1$$ $$9/7$$ $$15/7$$
Mean $$=\sum x p(x)=\dfrac{9}{7}$$
variance$$=\sum x^2\cdot p(x)-(\sum x.p(x))^2=\dfrac{15}{7}-\dfrac{81}{49}=\dfrac{24}{49}$$.
Question 7
1 / -0

The largest value in the collection of data is $$7.44$$. If the range is $$2.26$$, then find the smallest value in the collection

A
$$5.18$$

B
$$9.70$$

C
$$2.26$$

D
$$1.13$$

Solution

Let the data collection is represented by $$[X,7.44]$$,
where $$X$$ is the smallest value of data.
Range $$=2.26$$
$$\Rightarrow X=\text{largest value -Range}= 7.44-2.26=5.18$$
Question 8
1 / -0

The mean deviation about median for the following data is 4.4.calculate value of $$x$$
$$2,3,x,10,17$$.

A
$$3$$

B
$$5$$

C
$$7$$

D
$$17$$

Solution

Median $$=$$ $$\dfrac{N+1}{2}$$ $$=$$ 3rd term

$$\Rightarrow x$$ is median

Mean Deviation $$=$$ $$\dfrac{1}{N} \sum fi |Xi-M|$$

$$4.4 = \dfrac{|2-x| + |3-x| + |x-10| + |x-17|}{5}$$

Now as $$x > 2$$

$$|x-2|$$ $$=$$ $$x-2$$
$$22 =$$ $$x-2 + |3-x+10-x+17-x|$$
$$22 =$$ $$x-3x-2+30$$
$$2x=6$$
$$x=3$$
Question 9
1 / -0

Find the mean deviation about the mean as well as the coefficient of Mean Deviation about mean of the following set data:$$ 4, 7, 14, 11, 9$$.

A
$$2.8$$ and $$0.311$$

B
$$2.1$$ and $$0.211$$

C
$$24.8$$ and $$0.411$$

D
$$21.3$$ and$$0.566$$

Solution

Mean of the following set of data can be calculated by $$(\bar{x})=\dfrac{4+7+14+11+9}{5}=\dfrac{45}{5}=9$$

$$x_i$$ $$\bar{x}-x_i$$ $$|\bar{x}-x_i|$$
$$4$$ $$9-4=5$$ $$|5|=5$$
$$7$$ $$9-7=2$$ $$|2|=2$$
$$14$$ $$14-9=-5$$ $$|-5|=5$$
$$11$$ $$11-9=-2$$ $$|-2|=2$$
$$9$$ $$9-9=0$$ $$ |0|=0$$
Mean Deviation can be calcuated by (M.D) $$=\dfrac{\sum |\bar{x}-x_i|}{n}=\dfrac{5+2+5+2+0}{5}=\dfrac{14}{5}=2.8$$

Coefficient of Mean Deviation about mean can be calculated by $$=\dfrac{M.D}{Mean \enspace (\bar{x})}=\dfrac{2.8}{9}=0.311$$
Question 10
1 / -0

If mean deviation about Mean of a particular data consisting $$10$$ observations is$$7$$, then what will be value of mean deviation when each is multiplied by $$5$$?

A
$$35$$

B
$$45$$

C
$$55$$

D
$$65$$

Solution

Suppose original numbers were : x1 , x2, x3, ……, xn
Thus, $$(x1+x2+x3+…….+xn)/n = 10$$ (by the very definition of mean
After adding 1 to each number, the sum would be : 5$$\times$$ $$(x1+x2+x3+…….+xn) + n$$

Thus new mean would be: $$(5\times(x1+x2+x3+…….+xn) + n)/n = 5\times10 +1 = 51$$

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$$x_i$$	$$\bar{x}-x_i$$	$$\|\bar{x}-x_i\|$$
$$4$$	$$9-4=5$$	$$\|5\|=5$$
$$7$$	$$9-7=2$$	$$\|2\|=2$$
$$14$$	$$14-9=-5$$	$$\|-5\|=5$$
$$11$$	$$11-9=-2$$	$$\|-2\|=2$$
$$9$$	$$9-9=0$$	$$ \|0\|=0$$

Statistics Test - 37

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Statistics Test - 37

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SHARING IS CARING

Question 1

Range is rigidly defined.

Range can be calculated for open-ended intervals.

Range is not based on all the terms of a given data.

Range does not give a clear picture of variation in Data.

Solution

Question 2

Helpful in use of further statistical analysis as in regression, correlation etc.

Reliability of measure of central tendency

Control of variability

All of the above

Solution

Question 3

3.3

7.8

5.6

12.1

Solution

Question 4

Standard Deviation,Median,Range

Standard Deviation,Mode,Range

Standard Deviation,Variance,Range

Mean,Mode,Median

Solution

Question 5

Percentile, Quartile, Median

Median,Mode, Percentile

Percentile, Quartile, Mode

Mean,Mode, Median

Solution

Question 6

$$\dfrac {9}{7}, \dfrac {24}{49}$$

$$\dfrac {9}{7}, \dfrac {25}{48}$$

$$\dfrac {9}{8}, \dfrac {24}{49}$$

$$\dfrac {9}{8}, \dfrac {24}{48}$$

Solution

Question 7

$$5.18$$

$$9.70$$

$$2.26$$

$$1.13$$

Solution

Question 8

$$3$$

$$5$$

$$7$$

$$17$$

Solution

Question 9

$$2.8$$ and $$0.311$$

$$2.1$$ and $$0.211$$

$$24.8$$ and $$0.411$$

$$21.3$$ and$$0.566$$

Solution

Question 10

$$35$$

$$45$$

$$55$$

$$65$$

Solution

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