No. Think of these two situations:

a) we have the numbers 0, 2, 3, 5, 5. The mean and the median are both 3

b) we have the numbers 0, 0, 3, 5, 7. The mean and the median are both 3

In both cases the mean and the median are 3, but the mode differs. The mean and the median do not uniquely determine the mode.

No. Think of these two situations:

a) we have the numbers 0, 2, 3, 5, 5. The mean and the median are both 3

b) we have the numbers 0, 0, 3, 5, 7. The mean and the median are both 3

In both cases the mean and the median are 3, but the mode differs. The mean and the median do not uniquely determine the mode.

No, since the methods of calculating the three measures are different.

Definitely, there is not any equation to combine between them as mode, mean, and median are different measurements of a data set. the only correct solution is to find the median either graphically or mathematically of the data set.

Best regards

Thank you all for your assist, but actually I found this model in a text book, I don't know whether it is correct or not.

@Wulf Rehder

Thank you so much for your clarificatio, I highly appreciate your effort.

Regards

Mode =

d 1

( L m + --------------- * I )

d 1 + d 2

** in grouped data (measure of central tendency)

L m or L 1: lower limit of the model class

d 1 : diff between frequency of model class and the preceding class

d 2 : diff bet frequency of model class and following class

I or C : class interval or amount of class interval

dear Deeman

I hope this formula also help you. thx

Dear Wulf ,

class interval - frequency ( f ) - x - frequency * x (fx) - cummulative freq

12 - -- 2 -- 13 -- 26 -- 2

14 - -- 5 -- 15 -- 75 -- 7

16 - -- 17 -- 17 -- 289 -- 24

18 - -- 36 -- 19 -- 684 -- 60

20 - -- 17 -- 21 -- 357 -- 77

22 - -- 9 -- 23 -- 207 -- 86

24 - -- 3 -- 25 -- 75 -- 89

26 - 28 -- 1 -- 27 -- 27 -- 90

L 1 = 18

d 1 = 36 - 17 preceding frequency = 19

d 2 = 36 - 17 following frequency = 19

I = 2

Mode according to the formula = 18 + ( 19 / 38 * 2 )

= 18 + 1 = 19

X observation , can be calculated in the previous example by :

12 + 14 / 2 = 13 and so on

X` (mean) = summation fx / n = summation of frequency * x / n

n = summation of frequency = 90

summation of frequency * x / n = 1740

so X` = 1740 / 90 = 19.33

Median

L = lower limit of median class interval

f = frequency of median class interval

I = amount of of class interval

K = cummulative frequency of the of median class interval

Median = 18 + ( 90 - 2 * 24 / 2 * 36 * 2 )

= 18 + ( 42 / 72 * 2 )

= 18 + 1.17

= 19.17

** And according to Normal ( Gaussian ) distribution criteria : Mean = Median = Mode approximately.

====================================

Another example

class interval -- frequency

10- -- 8

20- -- 11

30- -- 15

40- -- 12

50- -- 10

60- -- 4

L 1 = 30

d 1 = 15 - 11 = 4

d 2 = 15 - 12 = 3

C or I = 10

Mode = 30 + ( 4 / 7 * 10 )

= 30 + ( 40 / 7 ) = 30 + 5 .71 = 35.71

Formula of class interval

Regarding references :-

** I don`t have the text book that was with my prof. Ahmed Hani in Assiut Uni , Egypt ( Prof of Statistics , Public Health )...

Thank you doctor Wulf . I appreciate your clarification. And I was need to put those formulas for assistance.

Thank you all dear colleagues for your cooperation, I highly appreciate your efforts.

I do agree with Deeman Yousif Mahmood.

However, I like to give a more accurate answer.

For a symmetric distribution, mean, median and mode are equal.

If the distribution is moderately asymmetrical, mean, median and mode follows the empirical relationship (due to Kearl Pearson)

3 (mean - median) = mean - mode

Note that this relationship is empirical but not theoretical

This means that this relationship can not give the exact value of mode but can give an estimated value of mode.

Thus, this formula can be used to find an estimated value of mode from known values of mean and median.