Measures of Central Tendency Test

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Measures of Central Tendency Test - 45

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Weekly Quiz Competition

Question 1
1 / -0

The most commonly used measure of central tendency is________.

A
AM

B
Media

C
Mode

D
GM and HM

Solution

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data. It is the most commonly used measure of central tendency because it includes all the observation in a given data and in comparison to other measures of central tendency, arithmetic mean has very simple application.
Question 2
1 / -0

The words 'means' or 'average' refers to ____________.

A
Arithmetic Mean

B
Geometric Mean

C
Harmonic Mean

D
All of above

Solution

Average or mean refers to all such average where a figure is taken out through mathematical methods from the a given series that represents the whole series. These average includes arithmetic mean, geometric mean and harmonic mean.
Question 3
1 / -0

Which of the following statements is true?

A
Usually mean is the best measure of central tendency

B
Usually median is the best measure of central tendency

C
Usually mode is the best measure of central tendency

D
Normally, GM is the best measure of central tendency

Solution

Arithmetic 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. It is considered as the best measure of central tendency because it includes all the observations of a series and the method as very simple application compared to other measures of central tendency.
Question 4
1 / -0

__________ is defined as the sum of observations divided by the number of observations.

A
Harmonic Mean

B
Geometric Mean

C
Arithmetic Mean

D
All of above

Solution

Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data. The formula of to calculate arithmetic mean is sd/N where sd is the summation of all the observations in the data and N is the number of observations in the data.
Question 5
1 / -0

Which of the following statement(s) is/ are false?

A
Mean is rigidly defined

B
Mean is not affected by due to sampling fluctuation

C
Mean has some mathematical properties

D
All of above

Solution

$$\textbf{Step -1: Analyze the options}$$

$$\text{The definition of mean is:}$$

$$\text{Mean = } \dfrac{\text{Sum of all observations}}{\text{Total number of observations}}$$

$$\text{Hence, it is clear that mean includes each and every value in the given sample.}$$

$$\text{Thus, fluctuations in any of the values in the sample space will affect the mean.}$$

$$\textbf{Step -2: Conclusion}$$

$$\text{Hence, the option that says mean is not affected by fluctuation of sample is incorrect.}$$

$$\textbf{Hence, the option which is false is (B).}$$
Question 6
1 / -0

_______ is used when most frequent occurring value if required. (discrete variable).

A
Mode

B
Mean

C
Median

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.
Question 7
1 / -0

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

A
It can be determined for a distribution with open ends

B
It is not based on all the observations

C
It is affected by extreme observations

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. 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 8

1 / -0

Consider 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	0−10	10−20	20−30	30−40
Frequency(f)	8	10	12	15
Class mark ( mid points= x)	5	15	25	35
Fx	40	150	300	525

Mean = summation of fx / summation of f

= 1015/ 45

= 22.55

Question 9
1 / -0

The average rainfall for a week, excluding Sunday, was $$10\ \text{cms}$$. Due to heavy rainfall on Sunday, the average for the week rose to $$15\ \text{cms}$$. How much rainfall was on Sunday?

A
$$25\ \text{cms}$$

B
$$35\ \text{cms}$$

C
$$45\ \text{cms}$$

D
$$55\ \text{cms}$$

Solution
Question 10
1 / -0

The relationship between mean, median and mode is ______________.

A
$$2\ Mean = 3\ Median - Mode$$

B
$$Mean = \dfrac {3\ Median - Mode}{2}$$

C
$$Median = \dfrac {2\ Mean + Mode}{3}$$

D
All of above

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.
Median is the middle most value of a series.
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.
The relationship between mean, median and mode is described as
Mode = 3 Median - 2 Mean
=> 2 mean = 3 median - mode
=> mean = ( 3 median - mode )/2
or
Mode = 3 Median - 2 Mean
=> 3 median = 2 mean + mode
=> median = ( 2 mean + mode )/3

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Re-Attempt Weekly Quiz Competition

Measures of Central Tendency Test - 45

Result

Measures of Central Tendency Test - 45

Score

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Rank

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SHARING IS CARING

Question 1

AM

Media

Mode

GM and HM

Solution

Question 2

Arithmetic Mean

Geometric Mean

Harmonic Mean

All of above

Solution

Question 3

Usually mean is the best measure of central tendency

Usually median is the best measure of central tendency

Usually mode is the best measure of central tendency

Normally, GM is the best measure of central tendency

Solution

Question 4

Harmonic Mean

Geometric Mean

Arithmetic Mean

All of above

Solution

Question 5

Mean is rigidly defined

Mean is not affected by due to sampling fluctuation

Mean has some mathematical properties

All of above

Solution

Question 6

Mode

Mean

Median

None of above

Solution

Question 7

It can be determined for a distribution with open ends

It is not based on all the observations

It is affected by extreme observations

All of above

Solution

Question 8

$$39.65$$

$$22.55$$

$$32.55$$

$$23.56$$

Solution

Question 9

$$25\ \text{cms}$$

$$35\ \text{cms}$$

$$45\ \text{cms}$$

$$55\ \text{cms}$$

Solution

Question 10

$$2\ Mean = 3\ Median - Mode$$

$$Mean = \dfrac {3\ Median - Mode}{2}$$

$$Median = \dfrac {2\ Mean + Mode}{3}$$

All of above

Solution

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