Empirical Relationship of the three measures of central tendency

Q. Show that the mode of the series obtained by combining the two series $S_1$ and $S_2$ given below is different from that of $S_1$ and $S_2$ taken separately:

$S_1$ : 3, 5, 8, 8, 9, 12, 13, 9, 9
$S_2$ : 7, 4, 7, 8, 7, 8, 13

Q. If the mode of a series exceeds its mean by 24, then mode exceeds median by:

1. 4
2. 8
3. 12
4. 16

Q.

The relation between mean, mode and median is

(a) $mode=(3\times mean)-(2\times median)$

(b)$mode=(3\times median)-(2\times mean)$

(c) $median=(3\times mean)-(2\times mode)$

(d) $mean=(3\times median)-(2\times mode)$

Q. Consider the following statements :
(a) Mode can be computed from histogram.
(b) Median is not independent of change of scale.
(c) Variance is independent of change of origin and scale.
Which of these is/are correct?

1. only (a) and (b)
2. only (a)
3. (a), (b) and (c)
4. only (b)

Q.

Let say if the mode of a series exceeds its mean by 24, then the mode exceeds median by:

1. 4

2. 8

3. 16

4. 12

Q.

Assertion: (A) In a graphical representation, if p times the distance between the Median and Mean is thrice the distance between Mode and Mean, then the value of p is 9.
Reason: (R) Mode= 3 Median - 2 Mean
Which of the following is true?

1. (A) and (R) are true and (R) is the correct explanation of (A)

2. (A) is false and (R) is the correct explanation of (A)

3. (A) is true and (R) is false

4. Both (A) and (R) are false

Q. If the mode of a series exceeds its mean by 24, then mode exceeds median by:

1. 16
2. 12
3. 4
4. 8

Q. Assertion: (A) In a graphical representation, if P times the distance between the median and mean is thrice the distance between mode and mean, then the value of p is 9.
Reason: (R) Mode= 3 Median - 2 Mean
Which of the following is true?

1. (A) and (R) are true and (R) is the correct explanation of (A)
2. (A) is false and (R) is the correct explanation of (A)
3. (A) is true and (R) is false
4. Both (A) and (R) are false

Q. If the difference of Mode and Median of a data is $24$, then the difference of Median and Mean is

1. $24$
2. $12$
3. $36$
4. $8$