Measures of Central Tendency Test

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Measures of Central Tendency Test - 48

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Question 1
1 / -0

The average (arithmetic mean) of a set of seven numbers is $$8$$. When an eighth number is added to the set, the average of the eight numbers is still $$8$$. What number was added to the set?

A
$$6$$

B
$$7$$

C
$$8$$

D
$$9$$
Question 2
1 / -0

Following is arranged in ascending order. If the median of the data is $$63$$, find the volume of x in a series $$29, 32, 48, 50, x, x+2, 72, 78, 84, 95$$.

A
$$60$$

B
$$62$$

C
$$63$$

D
$$64$$

Solution

Median is the middle most value of a series. So when the series has odd number of elements then median can be calculated easily but when the series has even number of elements then the series has two middle values, so median is calculated by taking out the average of both the value.

The series is first arranged into either ascending or descending order. The formula to calculate median = (N+1) /2 th term of the series where N is the number of observation in the series.
The given series is first arranged into ascending; 29,32,48,50,x,x+2,72,78,84,95

N= 10
median=> (10+1)/2 th term = 63
=> 11/2 th term = 63
=> 5.5 th term = 63
=> ( value of 5th term + value of 6th term)/2= 63

=> {x+( x+2)} /2 =63
=> 2x+2 = 126
=> 2x = 124
=> x= 62
Question 3
1 / -0

The formulae for calculating the median if individual observations are given will be.

A
$$(N+1)/2$$th if n is add

B
$$(N+1)th/2$$ if n is even

C
$$(N/2)$$th if n is even

D
Both a & c

Solution

Median is the middle most value of a series. So when the series has odd number of elements then median can be calculated easily but when the series has even number of elements then the series has two middle values, so median is calculated by taking out the average of both the value.

The series is first arranged into either ascending or descending order. The formula to calculate median = (N+1) /2 th term of the series in case odd numbers of data and median = N/2th term of the series in case even number of data where N is the number of observation in the series.
Question 4
1 / -0

The arithmetic mean between $$\cfrac { x+a }{ x } $$ and $$\cfrac { x-a }{ x } $$ when $$x\ne 0$$, is (the symbol $$\ne$$ means "not equal to"):

A
$$2$$, if $$a\ne 0$$

B
$$1$$

C
$$1$$, only if $$a=0$$

D
$$\dfrac {a}{x}$$

E
$$x$$

Solution

The arithmetic mean between two quantities is given by,
A.M.=$$\dfrac{\dfrac{x+a}{x}+\dfrac{x-a}{x}}{2}$$
=$$\dfrac{x+a+x-a}{2x}$$
=$$\dfrac{2x}{2x}$$
=1
Hence A.M.=1

Question 5

1 / -0

Consider the following frequency distribution.

Class Intervals	$$0-10$$	$$10-20$$	$$20-30$$	$$30-40$$
Frequency	$$8$$	$$10$$	$$12$$	$$15$$

Arithmetic mean $$=$$?

$$39.65$$

$$22.55$$

$$32.55$$

$$23.56$$

Solution

Class Intervals	Mid-values(x)	Frequency(f)	fx
$$01-0$$	$$5$$	$$8$$	$$40$$
$$10-20$$	$$15$$	$$10$$	$$150$$
$$20-30$$	$$25$$	$$12$$	$$300$$
$$30-40$$	$$35$$	$$15$$	$$525$$
		$$\displaystyle\sum f=45$$	$$\displaystyle\sum fx =1,015$$

Arithmetic mean $$=\dfrac{1,015}{45}=22.55$$.

Question 6
1 / -0

Find the value of $$p$$, if the mean of the following distribution is $$20$$.
$$x$$: $$15$$ $$17$$ $$19$$ $$20+p$$ $$23$$
$$f$$: $$2$$ $$3$$ $$4$$ $$5p$$ $$6$$

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Mean =$$ \dfrac {\sum x_{i} f_{i}} {\sum f_{i}} $$

$$\Rightarrow $$mean =$$\dfrac {(15\times 2)+(17\times 3)+(19 \times 4)+((20+p) \times 5p)+(23 \times 6)}{2+3+4+5p+6}$$

$$\Rightarrow $$mean =$$\dfrac {30+51+76+(20+p)(5p)+138}{2+3+4+5p+6}=20$$

$$\Rightarrow 295+100p+5p^{2}=300+100p$$

$$\Rightarrow 5p^{2}=5$$

$$\Rightarrow p=1$$

Question 7

1 / -0

What is the value of mean for the following data.

Class interval	Frequency
$$350-369$$	$$15$$
$$370-389$$	$$27$$
$$390-409$$	$$31$$
$$410-429$$	$$19$$
$$430-449$$	$$13$$
$$450-469$$	$$6$$

$$400$$

$$400.58$$

$$394$$

$$394.50$$

Solution

Class Intervals	Mid-values $$(x)$$	Frequency $$(f)$$	$$fx$$
$$350-369$$	$$359.5$$	$$15$$	$$5,392.5$$
$$370-389$$	$$379.5$$	$$27$$	$$10,246.5$$
$$390-409$$	$$399.5$$	$$31$$	$$12,384.5$$
$$410-429$$	$$419.5$$	$$19$$	$$7,970.5$$
$$430-449$$	$$439.5$$	$$13$$	$$5,713.5$$
$$450-469$$	$$459.5$$	$$6$$	$$2,757$$
		$$\displaystyle\sum f = 111$$	$$\displaystyle\sum fx = 44,464.5$$

Arithmetic mean $$= \cfrac{44,464.5}{111} = 400.58$$

Question 8

1 / -0

The following is the distribution of weekly wages of workers in a factory. Calculate the arithmetic mean of the distribution.

Weekly Wages (Rs.)	No. of Workers
$$240-269$$	$$7$$
$$270-299$$	$$19$$
$$300-329$$	$$27$$
$$330-359$$	$$15$$
$$360-389$$	$$12$$
$$390-419$$	$$12$$
$$420-449$$	$$8$$

$$352.3$$

$$344.5$$

$$226.7$$

$$336.7$$

Solution

Class Intervals	Mid-values (x)	Frequency(f)	fx
$$240-269$$	$$254.5$$	$$7$$	$$1,781.5$$
$$270-299$$	$$284.5$$	$$19$$	$$5,405.5$$
$$300-329$$	$$314.5$$	$$27$$	$$8,491.5$$
$$330-359$$	$$344.5$$	$$15$$	$$5,167.5$$
$$360-389$$	$$374.5$$	$$12$$	$$4,494$$
$$390-419$$	$$404.5$$	$$12$$	$$4,854$$
$$420-449$$	$$434.5$$	$$8$$	$$3,476$$
		$$\displaystyle\sum f=100$$	$$\displaystyle\sum fx=33,670$$

Arithmetic mean $$=33,670/100=336.7$$.

Question 9
1 / -0

The median of $$0.05,0.50,0.055,0.505\ and\ 0.55$$ is

A
$$0.05$$

B
$$0.505$$

C
$$0.50$$

D
$$0.055$$

Solution

$$\Rightarrow$$ The median is the middle number in a group of numbers.
$$\Rightarrow$$ The given numbers are $$0.05,\,0.50,\,0.055,\,0.505,\,0.55$$
$$\Rightarrow$$ Now, arranging given numbers in ascending order we get, $$0.05,\,0.055,\,0.50,\,0.505,\,0.55$$
$$\Rightarrow$$ So, here we can see middle number is $$0.50$$.
$$\therefore$$ Median is $$0.50$$
Question 10
1 / -0

Find the mode of the given set;
$$3$$, $$5$$, $$9$$, $$6$$, $$5$$, $$9$$, $$2$$, $$9$$, $$3$$ and $$5$$

A
$$5$$

B
$$9$$

C
$$5$$ and $$9$$

D
$$5$$,$$6$$ and $$9$$

Solution

$$Mode=$$no of $$element$$ which is repeated more.
$$Mode=5$$ and $$9$$
$$\because $$ Both are repeated $$3$$ times in the series.

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$$x$$:	$$15$$	$$17$$	$$19$$	$$20+p$$	$$23$$
$$f$$:	$$2$$	$$3$$	$$4$$	$$5p$$	$$6$$

Measures of Central Tendency Test - 48

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Measures of Central Tendency Test - 48

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Question 1

$$6$$

$$7$$

$$8$$

$$9$$

Question 2

$$60$$

$$62$$

$$63$$

$$64$$

Solution

Question 3

$$(N+1)/2$$th if n is add

$$(N+1)th/2$$ if n is even

$$(N/2)$$th if n is even

Both a & c

Solution

Question 4

$$2$$, if $$a\ne 0$$

$$1$$

$$1$$, only if $$a=0$$

$$\dfrac {a}{x}$$

$$x$$

Solution

Question 5

$$39.65$$

$$22.55$$

$$32.55$$

$$23.56$$

Solution

Question 6

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 7

$$400$$

$$400.58$$

$$394$$

$$394.50$$

Solution

Question 8

$$352.3$$

$$344.5$$

$$226.7$$

$$336.7$$

Solution

Question 9

$$0.05$$

$$0.505$$

$$0.50$$

$$0.055$$

Solution

Question 10

$$5$$

$$9$$

$$5$$ and $$9$$

$$5$$,$$6$$ and $$9$$

Solution

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