Measures of Central Tendency Test

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Measures of Central Tendency Test - 46

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Weekly Quiz Competition

Question 1
1 / -0

_______ is that value of the variant which repeats maximum number of times in a distribution and around which other observations are densely distributed.

A
Mean

B
Median

C
Harmonic mean

D
Mode

Solution

Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value.
Question 2
1 / -0

The average marks of three batches of students having 70, 50 and 30 students respectively are 50, 55 and 45. Find the average marks of all the 150 students, taken together.

A
$$50.67$$

B
$$40.67$$

C
$$50.60$$

D
$$40.60$$

Solution

Given that, the average marks of 70, 50 and 30 students respectively are 50, 55 and 45 marks.
$$\therefore\ $$ the total marks of 70, 50 and 30 students will be,
$$70 \times 50, 50 \times 55$$ and $$30 \times 45$$ respectively.
The average marks of all the 150 students will be:
$$= \dfrac{ (3500 + 2750 + 1350 )}{( 70+50+30)}$$ $$\left[\text{Average}=\dfrac{\text{Sum of all quantities}}{\text{Number of quantities}}\right]$$
$$\Rightarrow \dfrac{7,600 }{150}$$
$$\Rightarrow 50.67$$

Hence, the average marks of all the 150 students, taken together are $$50.67$$
Question 3
1 / -0

Which of the following sentence is/ are wrong in relation to 'Mode'?

A
It is not affected by extreme observations

B
It can be determined even for a distribution

C
It cannot be located graphically

D
All of above

Solution

Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value. Mode can be allocated graphically through bar diagrams as mode will be the highest bar in a bar graph as it occurs the highest number of times.
Question 4
1 / -0

Extreme values have _______ effect on mode.

A
a large

B
a small

C
no

D
None of above

Solution

Mode is the highest occurring figure in a series. It is the value in a series of observation that repeats maximum number of times and which represents the whole series as most of the values in the series revolves around this value. Therefore, it is a positional average and it is not affected by the extreme values of the series as it is value within the series that occurs highest number of times.
Question 5
1 / -0

Consider the following observation relating to marks obtained by $$10$$ students in CS Foundation Exam: $$201, 202, 207, 222, 276, 201, 246, 212, 285, 312$$.
Arithmetic mean $$=$$?

A
$$206$$

B
$$237.3$$

C
$$217.2$$

D
$$216.1$$

Solution

Mean refers to the average amount in a given group of data. In this measure of central tendency, all the data are added up and then divided by the number of figures in the data in order to ascertain the mean.

Mean $$\dfrac{(201+ 202+207+222+276+201+246+212+285+312}{10}$$
$$= 236.4 $$
Question 6
1 / -0

The following table gives the marks obtained by $$300$$ students of a management course. Find the median of the distribution.
Marks obtained No. of students
$$0 - 15$$ $$26$$
$$15 - 30$$ $$34$$
$$30 - 45$$ $$64$$
$$45 - 60$$ $$76$$
$$60 - 75$$ $$60$$
$$75 - 90$$ $$60$$
$$90 - 100$$ $$10$$

A
$$62.96$$ marks

B
$$62.13$$ marks

C
$$50.13$$ marks

D
$$50.96$$ marks
Solution
Median is the middle most value of a given series that represents the whole class of the series. For a group data,
Median = L + [{(n/2) – B}/G] × w where
L is the lower class boundary of the group containing the median
n is the total number of values
B is the cumulative frequency of the groups before the median group
G is the frequency of the median group
w is the group width
Since the median is the middle value, which in this case is 165th one , which is in the 45-60 group. Therefore , 45-60 is the median group so
L = 45
n = 330
B = 26 + 34 + 64 = 124
G = 76
w = 15
Median= 45 + [{(330/2) – 124}/76] × 15
= 45 + 8.09
= 53.09
Question 7
1 / -0

$$10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23$$
The median of the observations above is _________.

A
$$17.55$$

B
$$18$$

C
$$15$$

D
$$16.5$$

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; 10,14,15,16,18,18,18,19,20,22,23.

N= 11

median= (11+1)/2 th term = 12/2 th term = 6 th term = 18
Question 8
1 / -0

The numerical value separating the higher half of a sample from a lower half is?

A
Median

B
Mode

C
Mean

D
Standard deviation

Solution

Median is the middle most value of a series. So it divides a series of observations into two equal parts where 50% of the observations are below the median value and other 50% are above the median value.
Question 9
1 / -0

The average of five numbers is $$40$$ and the average of another six numbers is $$50$$. The average of all numbers taken together is _______.

A
$$44.44$$

B
$$45.00$$

C
$$45.45$$

D
$$90.00$$

Solution

The average of five numbers is 40 , so the total of these five numbers will be 5x40.
The average of another six numbers is 50 , so the total of these six numbers will be 6x50.
Therefore, the average of all these taken together will be
$$= \dfrac{( 200+ 300)}{5+6}$$
$$= \dfrac{500}{11 }$$
$$= 45.45 $$
Question 10
1 / -0

Which of the following statements about the median is NOT true?

A
It is more affected by extreme values than the mean

B
It is the middle value that separates the upper half from the lower half

C
It is equal to the mode in bell-shaped distributions

D
Both b & c

Solution

Median is the middle most value of a given series that represents the whole class of the series.So since it is a positional average, it is calculated by observation of a series and not through the extreme values of the series which. Therefore, median is not affected by the extreme values of a series

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Marks obtained	No. of students
$$0 - 15$$	$$26$$
$$15 - 30$$	$$34$$
$$30 - 45$$	$$64$$
$$45 - 60$$	$$76$$
$$60 - 75$$	$$60$$
$$75 - 90$$	$$60$$
$$90 - 100$$	$$10$$

Measures of Central Tendency Test - 46

Result

Measures of Central Tendency Test - 46

Score

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Rank

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SHARING IS CARING

Question 1

Mean

Median

Harmonic mean

Mode

Solution

Question 2

$$50.67$$

$$40.67$$

$$50.60$$

$$40.60$$

Solution

Question 3

It is not affected by extreme observations

It can be determined even for a distribution

It cannot be located graphically

All of above

Solution

Question 4

a large

a small

no

None of above

Solution

Question 5

$$206$$

$$237.3$$

$$217.2$$

$$216.1$$

Solution

Question 6

$$62.96$$ marks

$$62.13$$ marks

$$50.13$$ marks

$$50.96$$ marks

Solution

Question 7

$$17.55$$

$$18$$

$$15$$

$$16.5$$

Solution

Question 8

Median

Mode

Mean

Standard deviation

Solution

Question 9

$$44.44$$

$$45.00$$

$$45.45$$

$$90.00$$

Solution

Question 10

It is more affected by extreme values than the mean

It is the middle value that separates the upper half from the lower half

It is equal to the mode in bell-shaped distributions

Both b & c

Solution

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