Measures of Central Tendency Test

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Measures of Central Tendency Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

If a variable takes discrete values $$x+4, \space x-\displaystyle\frac{7}{2}, \space x-\displaystyle\frac{5}{2}, \space x-3, \space x-2, \space x+\displaystyle\frac{1}{2}, \space x-\displaystyle\frac{1}{2}, \space x+5, \space (x>0)$$ then the median is

A
$$x - \displaystyle\frac{5}{4}$$

B
$$x - \displaystyle\frac{1}{2}$$

C
$$x-2$$

D
$$x + \displaystyle\frac{5}{4}$$

Solution

Given data's are, $$x+4, \space x-\displaystyle\frac{7}{2}, \space x-\displaystyle\frac{5}{2}, \space x-3, \space x-2, \space x+\displaystyle\frac{1}{2}, \space x-\displaystyle\frac{1}{2}, \space x+5, \space (x>0)$$
Now arranging in ascending order, $$
\space x-\displaystyle\frac{7}{2},
\space x-3
,\space x-\displaystyle\frac{5}{2} ,
\space x-2,
\space x-\displaystyle\frac{1}{2},
\space x+\displaystyle\frac{1}{2}, x+4,
\space x+5$$
Hence required mean $$=$$ mean of $$4^{th}$$ and $$5^{th}$$ term $$=x-\cfrac{5}{4}$$ (Since number of terms are even.)
Question 2
1 / -0

The median of the data $$5,6,7,8,9,10$$ is

A
$$7$$

B
$$8$$

C
$$7.5$$

D
$$8.5$$

Solution

There are six observations

$$\therefore \quad $$ Median = $$AM$$ of $$3^{rd}$$ and $$4^{th}$$ observation

$$\Rightarrow \quad \mbox{Median} = \displaystyle\frac{7+8}{2} = 7.5$$
Question 3
1 / -0

Find the mode of:
$$5, 6, 9, 13, 6, 5, 6, 7, 6, 6, 3$$

A
$$6$$

B
$$7$$

C
$$9$$

D

Solution

Given series is $$5,6,9,13,6,5,6,7,6,6,3$$
Here digit $$6$$ is repeated five times.
Hence, here mode is $$6$$.
Question 4
1 / -0

The mode of the following data:
$$120,110,130,110,120,140,130,120,140,120$$ is

A
$$110$$

B
$$120$$

C
$$130$$

D
$$115$$

Solution

The frequency table for the given data is as given below

Value $$(x_i)$$ $$110$$ $$120$$ $$130$$ $$140$$
Frequency $$(f_i)$$ $$2$$ $$4$$ $$2$$ $$2$$

We observe that the value $$120$$ has the maximum frequency. Hence, the mode or modal value is $$120$$.
Question 5
1 / -0

Find the mode of $$27,12,18,19, 18,24,17,18$$

A
$$17$$

B
$$18$$

C
$$19$$

D
$$20$$

Solution

The numbers are: $$27,12,18,19,18,24,17,18$$
Arranging in ascending order: $$12, 17, 18, 18, 18, 19, 24, 27$$
$$18$$ occurs $$3$$ times and maximum number of times. Hence, it is the mode.
Question 6
1 / -0

The mean of $$x + 3, x + 5, x + 7, x + 9$$ and $$x + 11$$ is

A
$$2x+7$$

B
$$x+8$$

C
$$x+7$$

D
None of these

Solution

The observations are : $$x+3,x+5,x+7,x+9, x+11$$
Mean = $$\dfrac{sum}{number \quad of \quad observations}$$ = $$\dfrac{x+3,x+5,x+7,x+9, x+11}{5}$$ = $$\dfrac{5x + 35}{5} = x + 7$$
Question 7
1 / -0

Ages of the employees of a company are given below. Find the mode.
Ages (in years) 22 23 25 19 21 27
Number of employees 14 19 17 27 12 15

A
$$18$$ years

B
$$19 $$ years

C
$$20$$ years

D
$$21$$ years

Solution

Maximum number of employees have age = 19 years.
Thus, 19 is the mode of the data
Question 8
1 / -0

Find the median of the following data:
$$9, 3, 20, 13, 0, 7$$ and $$10$$

A
$$7$$

B
$$9$$

C
$$10$$

D
None of these

Solution

Given data is $$9,3,20,13,0,7, 10$$
Arranging them in order, we get
$$0, 3, 7,9, 10,13,20$$
Median is the middle score in ordered data.
Therefore, here median is $$9$$.
Question 9
1 / -0

The ages of teachers of a school are
$$53, 37, 39, 51, 46, 42, 44, 47, 55, 48$$. Find the median

A
$$46.5$$

B
$$47.5$$

C
$$48.5$$

D
$$49.5$$

Solution

Age of teachers are: $$53, 37, 39, 51, 46, 42, 44, 47, 55, 48$$
Arranging in ascending order: $$37, 39, 42, 44, 46, 47, 48, 51, 53, 55$$
There are $$10$$ numbers, hence, the median will be the mean of $$\cfrac{n}{2}$$ and $$\cfrac{n}{2}+1$$ terms
Median $$=$$ mean of $$5^{th}$$ and $$6^{th}$$ terms
Median $$=$$ mean of $$46$$ and $$47$$
Median $$= \cfrac{46 + 47}{2}$$
Median $$= \cfrac{93}{2} = 46.5$$
Question 10
1 / -0

Find the median of the following data:
$$3.6, 9.4, 3.8, 5.6, 6.5, 8.9, 2.7, 10.8, 15.6, 1.9$$ and $$7.6.$$

A
$$4.5$$

B
$$5.5$$

C
$$6.5$$

D
$$7.5$$

Solution

Given data is $$3.6, 9.4, 3.8, 5.6, 6.5, 8.9, 2.7, 10.8, 15.6, 1.9, 7.6$$
Arranging them in ordered pair,
$$1.9, 2.7, 3.6, 3.8, 5.6, 6.5, 7.6, 8.9, 9.4, 10.8, 15.6$$.
Here, middle score is $$6.5$$.
Hence, median is $$6.5$$.

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Value $$(x_i)$$	$$110$$	$$120$$	$$130$$	$$140$$
Frequency $$(f_i)$$	$$2$$	$$4$$	$$2$$	$$2$$

Ages (in years)	22	23	25	19	21	27
Number of employees	14	19	17	27	12	15

Measures of Central Tendency Test - 9

Result

Measures of Central Tendency Test - 9

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Question 1

$$x - \displaystyle\frac{5}{4}$$

$$x - \displaystyle\frac{1}{2}$$

$$x-2$$

$$x + \displaystyle\frac{5}{4}$$

Solution

Question 2

$$7$$

$$8$$

$$7.5$$

$$8.5$$

Solution

Question 3

$$6$$

$$7$$

$$9$$

13

Solution

Question 4

$$110$$

$$120$$

$$130$$

$$115$$

Solution

Question 5

$$17$$

$$18$$

$$19$$

$$20$$

Solution

Question 6

$$2x+7$$

$$x+8$$

$$x+7$$

None of these

Solution

Question 7

$$18$$ years

$$19 $$ years

$$20$$ years

$$21$$ years

Solution

Question 8

$$7$$

$$9$$

$$10$$

None of these

Solution

Question 9

$$46.5$$

$$47.5$$

$$48.5$$

$$49.5$$

Solution

Question 10

$$4.5$$

$$5.5$$

$$6.5$$

$$7.5$$

Solution

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