Measures of Central Tendency Test

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Measures of Central Tendency Test - 43

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Weekly Quiz Competition

Question 1
1 / -0

In how many ways can 5 persons be seated at a round table so that two particular persons will be together?

A
12

B
120

C
720

D
180

Solution

The number of ways in which n number of people can arrange themselves at a round table is (n-1)! ways. The number of ways in which 5 people can arrange themselves at a round table is 4! ways. But considering 2 persons a single unit, the number of ways in which 5 people can arrange themselves at a round table is 3! ways. Now those two people can arrange themselves in 2! ways. So the answer will be 3! * 2! = 12 ways.
Question 2
1 / -0

The sum of the deviations of a set of values $$x_1, x_2$$, ...... $$x_n$$ measured from $$50$$ is $$-10$$ and the sum of deviations of the values from $$46$$ is $$70$$. The mean is ___________.

A
$$49$$

B
$$49.5$$

C
$$49.75$$

D
$$50$$

Solution

Sum of deviations from $$50$$ is $$-10$$

$$\Rightarrow \sum(xi - 50) = -10$$
$$\sum x_i - 50\sum1 = -10$$
$$\sum x_i - 50n = -10$$

$$\therefore y-50n=-10.....(1)$$

Sum of deviations from $$46$$ is $$70$$

$$\Rightarrow \sum(x_i - 46) = 70$$
$$\sum x_i - 46\sum1 = 70$$
$$\sum x_i - 46n = 70$$

$$\therefore y-46n=70.....(2)$$

Solving $$(1)$$ and $$(2)$$, we get
$$4n = 80$$ i.e. $$n=20$$

Putting value of $$n$$ in $$(1)$$, we get
$$y=990$$

Mean $$= \dfrac{\sum x_i}{n} = \dfrac{y}{n} = \dfrac{990}{20} = 49.5$$
Question 3
1 / -0

Sum of squares of deviation of $$10$$ observations measured from $$5$$ is $$17$$ and sum of squares of observations is $$170$$ then mean of observation is

A
$$40.3$$

B
$$4.5$$

C
$$4$$

D
$$4.03$$

E
$$4.3$$

Solution

$$x_1,x_2,x_3,x_4...x_10\\x_1^2+x_2^2+x_3^2+x_4^2+....x_10^2=17 (Given) \rightarrow (i)$$
$$(x_1-5)^2+(x_2-5)^2+(x_3-5)^2+....+(x_10-5)^2=17(Given)\rightarrow (i)$$
$$Mean (M)=\cfrac{x_1+x-2+x_3+....x_10}{10}\\ \Rightarrow x_1+x_2+x_3+....+x_10=10M\rightarrow(iii)$$
From equation $$(ii)$$ we get
$$x_1^2+25-10x_1+x_2^2+25-10x_2+x_3^2+25-10x_3+...+x_10^2+25-10x_10=17\\ \Rightarrow (x_1^2+x_2^2+....x_10^2)-10(x_1+x_2+x_3+....+x_10)+25\times10=17\\ \Rightarrow 170-10(10M)+250=17\\ \Rightarrow420-100M=17\\ \Rightarrow100M=403\\ \Rightarrow M=\cfrac{403}{100}=4.03$$
Question 4
1 / -0

A distribution, where the value of arithmetic mean is maximum as compared to median and mode, is

A
Normal distribution

B
Positively-skewed distribution

C
Negatively-skewed distribution

D
None of these
Question 5
1 / -0

Which of the following is true in relation to assumed mean method?

A
Any value, whether existing in the data or not, can be taken as assumed mean.

B
In order to simplify the calculation, centrally located value in the data can be selected as assumed mean.

C
Both A and B

D
None of these

Solution

In assumed mean method, any value can be taken as assumed mean whether it is there in the data or not but it should be centrally located in the data so that to simply the big figures in the data in order to ascertain mean of the given data through easy calculations.
Question 6
1 / -0

A measure of central tendency means -
I. Representative of a set of data.
II. A single figure which is representative of whole distribution.
III. An average of a distribution.

A
I

B
II

C
III

D
All of the above

Solution

Properties of a good measure of central tendency includes:
1. The figure should be representative of the data set, as only then is it beneficial for further analysis.
2. The figure should be representative of the whole distribution of the population, as only then is it possible to draw statistical inference about the population.
3. It should be an average of the distribution, as statistically, the average is where the maximum of the population will lie, and thus this value is most important.

The most common measures of central tendency include Mean, Median, Mode.
Question 7
1 / -0

Measures of central tendency for a given set of observations measures:
1. The scatteredness of the observations
2. The central location of the observations

Select the correct answer from the options given below.

A
$$1$$ only

B
$$2$$ only

C
Both $$1$$ and $$2$$

D
None of these

Solution

Measures of central tendency is a mathematical concept that measures the central most value of a given series which can represent the whole set of the series. In the given series, the central location of the observation is measured through different tools in order to ascertain the most efficient value that can represent the series.
Question 8
1 / -0

Which of these is not affected by extreme values?

A
Mean

B
Mode

C
Median

D
Standard deviation

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.
Question 9
1 / -0

Which of the following is a "Positional Average"?
I. Mean
II. Median
III. Mode
Select the correct answer from the options given below.

A
I and II

B
I and III

C
None of the (A), (B) or (D)

D
II and III

Solution

Positional average refers to the average which are taken out through observation from the series where a particular value from the series is picked up which represents the whole series. In median, the middle most value of the series is taken where in mode, the value which occurs the highest number of times is taken as the representative value.
Question 10
1 / -0

"An average is a single value within the range of data that is used to represent all values in the series. Since an average is somewhere within the range of the data, it is also called a measure of Central Value". This definition is given by _________________.

A
Croxton and Cowden

B
Simpson and Kafka

C
Clark and Sekkade

D
Murry R. Spiegal

Solution

Croxton and Cowden proposed a very universally accepted definition of measure of central tendency where they defined average as a single value which is within the range of the series that represents the whole series of observation and since the value is within the range of the series, it is usually called the measure of central tendency owing to its central value.

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Measures of Central Tendency Test - 43

Result

Measures of Central Tendency Test - 43

Score

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Rank

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SHARING IS CARING

Question 1

12

120

720

180

Solution

Question 2

$$49$$

$$49.5$$

$$49.75$$

$$50$$

Solution

Question 3

$$40.3$$

$$4.5$$

$$4$$

$$4.03$$

$$4.3$$

Solution

Question 4

Normal distribution

Positively-skewed distribution

Negatively-skewed distribution

None of these

Question 5

Any value, whether existing in the data or not, can be taken as assumed mean.

In order to simplify the calculation, centrally located value in the data can be selected as assumed mean.

Both A and B

None of these

Solution

Question 6

I

II

III

All of the above

Solution

Question 7

$$1$$ only

$$2$$ only

Both $$1$$ and $$2$$

None of these

Solution

Question 8

Mean

Mode

Median

Standard deviation

Solution

Question 9

I and II

I and III

None of the (A), (B) or (D)

II and III

Solution

Question 10

Croxton and Cowden

Simpson and Kafka

Clark and Sekkade

Murry R. Spiegal

Solution

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