Measures of Central Tendency Test

Result

Measures of Central Tendency Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

The weight ( in kg ) of $$5$$ men are $$62, 65, 69, 66$$ and $$61.$$ The median is

A
$$45$$ kg

B
$$66$$ kg

C
$$65$$ kg

D
$$55$$ kg

Solution

Arranging in the ascending order we have $$61, 62, 65, 66, 69.$$
Hence median$$=65$$ kg.
Question 2
1 / -0

The marks of 10 students in a certain subject in a class are 20, 19, 50, 48, 50, 36, 35, 50, 40, 40 The mean and mode are respectively as .............

A
Mean =38.8, Mode = 50

B
Mean = 40, Mode= 35

C
Mean = 30, Mode= 33

D
Mean = 35, Mode= 25

Solution

$$\Rightarrow$$ Arranging given numbers in ascending order $$19,\,20,\,35,\,36,\,40,\,40,\,48,\,50,\,50,\,50$$.
$$\Rightarrow$$ Number of observation $$=10$$
$$\Rightarrow$$ $$Mean=\dfrac{19+20+35+36+40+40+48+50+50+50}{9}=\dfrac{388}{10}=38.8$$
$$\therefore$$ $$Mean=38.8$$
$$\Rightarrow$$ We can number $$50$$ occurs maximum times i.e. $$3$$ times.
$$\therefore$$ $$Mode=50$$
Question 3
1 / -0

Find the inter quartile range for the data: $$9,11,15,19,17,13,7.$$

A
$$7$$

B
$$6$$

C
$$8$$

D
None of the above

Solution

Interquartlie is the difference between upper quartile and lower quartile.
Lower quartile is the median of the lower half of the data set.
Upper quartile is the median of the upper half of the data set.
Given data set is $$9,11,15,19,17,13,7$$
Arranging the data set in ascending order we get $$7,9,11,13,15,17,19$$
Number of values in the data set is $$n=7$$

Lower quartile is given by $$Q_1=\dfrac{n+1}{4}=\dfrac{7+1}{4}=\dfrac{8}{4}=2^{nd} value$$

Therefore, the lower quartile is $$Q_1=9$$

Upper quartile is given by $$Q_3=\dfrac 34(n+1)=\dfrac 34(7+1)=\dfrac 34(8)=6^{th} value$$

Therefore, the upper quartile is $$Q_3=17$$

Therefore, the inter quartile is given by $$Q_3-Q_1=17-9=8$$
Question 4
1 / -0

The mode of the distribution $$3, 5, 7, 4, 2, 1, 4, 3, 4$$ is

A
$$7$$

B
$$4$$

C
$$3$$

D
$$1$$

Solution

Observation Frequency
$$3$$ $$2$$
$$5$$ $$1$$
$$7$$ $$1$$
$$4$$ $$3$$
$$2$$ $$1$$
$$1$$ $$1$$

$$4$$ has the highest frequency of $$3$$. So $$4$$ is the mode
Question 5
1 / -0

What is the average of squares of consecutive odd numbers between $$1$$ and $$13 $$?

A
$$49$$

B
$$51$$

C
$$53$$

D
$$57$$

Solution

The consecutive odd numbers from $$1$$ to $$13 = 3, 5, 7, 9, 11$$
Thus required average = $$\displaystyle \frac{3^{2}+5^{2}+7^{2}+9^{2}+11^{2}}{5}=\frac{9+25+49+81+121}{5}=\frac{285}{5}=57$$
Question 6
1 / -0

Find the lower quartile for the data: $$9,11,15,19,17,13,7$$.

A
$$7$$

B
$$9$$

C
$$13$$

D
None of the above

Solution

Lower quartile is the median of the lower half of the data set.
Given data set is $$9,11,15,19,17,13,7$$
Arranging the data set in ascending order we get $$7,9,11,13,15,17,19$$
Number of values in the data set is $$n=7$$

Lower quartile is given by $$Q_1=\dfrac{n+1}{4}=\dfrac{7+1}{4}=\dfrac{8}{4}=2^{nd} value$$

Therefore, the lower quartile is $$9$$
Question 7
1 / -0

Construction of a cumulative frequency table is useful in determining the

A
mean

B
median

C
mode

D
all the above three measures

Solution

A cumulative frequency table helps to determine the median of the series.
Question 8
1 / -0

The mode of a set of observations is the value which

A
occurs most frequently

B
is central

C
is between maximum and minimum

D
none of the foregoing

Solution

By definition, mode is the value which occurs most frequently.
Question 9
1 / -0

The daily earnings ( in rupees ) of $$10$$ workers in a factory are $$8, 16, 19, 8, 16, 19, 16, 8, 19, 16.$$ The median wage is ,

A
Rs. $$17.50$$

B
Rs. $$8.00$$

C
Rs. $$19.00$$

D
Rs. $$16.00$$

Solution

Arranging the daily earnings in ascending order, we have $$8, 8, 8, 16, 16, 16, 16, 19, 19, 19.$$ The median is average of $$5^{th}$$ and $$6^{th}$$ wages, i.e., $$\displaystyle \frac{16+16}{2}=16$$.
Question 10
1 / -0

The average weight of 29 students is 28 kg. By the admission of a new student the average weight is reduced to 27.8 kg. The weight of the new student is

A
22 kg

B
21 kg

C
22.4 kg

D
21.6 kg

Solution

Weight of new student
$$\displaystyle = 30\times 27.8-29\times 28$$
$$\displaystyle = 834-812=22\ kg.$$

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Observation	Frequency
$$3$$	$$2$$
$$5$$	$$1$$
$$7$$	$$1$$
$$4$$	$$3$$
$$2$$	$$1$$
$$1$$	$$1$$

Measures of Central Tendency Test - 13

Result

Measures of Central Tendency Test - 13

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Question 1

$$45$$ kg

$$66$$ kg

$$65$$ kg

$$55$$ kg

Solution

Question 2

Mean =38.8, Mode = 50

Mean = 40, Mode= 35

Mean = 30, Mode= 33

Mean = 35, Mode= 25

Solution

Question 3

$$7$$

$$6$$

$$8$$

None of the above

Solution

Question 4

$$7$$

$$4$$

$$3$$

$$1$$

Solution

Question 5

$$49$$

$$51$$

$$53$$

$$57$$

Solution

Question 6

$$7$$

$$9$$

$$13$$

None of the above

Solution

Question 7

mean

median

mode

all the above three measures

Solution

Question 8

occurs most frequently

is central

is between maximum and minimum

none of the foregoing

Solution

Question 9

Rs. $$17.50$$

Rs. $$8.00$$

Rs. $$19.00$$

Rs. $$16.00$$

Solution

Question 10

22 kg

21 kg

22.4 kg

21.6 kg

Solution

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