Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

Q.

The relationship between Mean, Median and Mode is

1. 3Mode = 2 median - 3 mean

2. Median = Mean + Mode

3. Mode = 3 median - 2 mean

4. Mode = 2 median - 3 mean

Q.

Which measure of central tendency is not a good representative of the data when you have a few extreme values?

1. Median
2. Mode
3. Ogive
4. Mean

Q.

Which measure of central tendency will a shoe manufacturer make use of to determine the size(s) which he should manufacture in maximum quantity?

1. Mean

2. Median

3. Mode

4. Standard deviation

Q.

The average marks of the students in Mathematics of class $8^{th}$ is 45. But most of the students were given 60 out of 100.The Median of the class would be:

1. 30

2. 40

3. 50

4. 60

Q.

Mode is:

1. Mostfrequentvalue

2. Middlemostvalue

3. Leastfrequentvalue

4. None of these

Q.

Match the following
$\begin{array}{cc}\text{(i) Mean}& \text{A. Typical value}\\ \text{(ii) Median}& \text{B. Most popular value}\\ \text{(iii) Mode}& \text{C. Gets highly affected by extreme values}\end{array}$

1. (i)-A, (ii)-B, (iii)-C
2. (i)-B, (ii)-A, (iii)-C
3. (i)-C, (ii)-A, (iii)-B
4. (i)-B, (ii)-C, (iii)-A

Q.

The following are the marks obtained in Science by students in class X.
The mean of the given data is 63.33.
Is this mean an appropriate representation of the average marks obtained?
If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution?
What is the value of this measure of central tendency for the given data?

$\begin{array}{cc}Marks& Frequency\\ 10-20& 1\\ 20-30& 0\\ 30-40& 0\\ 40-50& 0\\ 50-60& 1\\ 60-70& 5\\ 70-80& 15\\ 80-90& 20\\ 90-100& 3\end{array}$

1. No, median, value of median = 80.12

2. No, mode, value of mode = 85

3. Yes, mean is the best measure of an average

4. Yes, the value of mean represents this data the best

Q.

Match the following
$\begin{array}{cc}\text{(i) Mean}& \text{A. Typical value}\\ \text{(ii) Median}& \text{B. Most popular value}\\ \text{(iii) Mode}& \text{C. Gets highly affected by extreme values}\end{array}$

1. (i)-B, (ii)-A, (iii)-C
2. (i)-C, (ii)-A, (iii)-B
3. (i)-B, (ii)-C, (iii)-A
4. (i)-A, (ii)-B, (iii)-C

Q. There are lottery tickets labelled with any of the numbers from 1 to 500. I want to find the number which is the most common in the lottery tickets. Which measures of central tendency do I need to use?

1. Median
2. Mean
3. Mode
4. None of the above

Q.

One of the methods of determining mode is :

1. Mode = 2 Median – 3 Mean

2. Mode = 2 Median + 3 Mean

3. Mode = 2 Median – 2 Mean

4. Mode = 3 Median + 2 mean