Question

The median and mode respectively of a frecuenc
distribution are 26 and 29. Then find its mean​

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{Median = 26} \\ &\sf{Mode = 29} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\:find-\begin{cases} &\sf{Mean}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline{\sf{Solution-}}$

Given that

• Median = 26

• Mode = 29

We know that

• Relationship between Mean, Mode and Median is given by Empirical Formula,

• Empirical Formula is given by

$\rm :\longmapsto\:Mode = 3Median - 2Mean$

On substituting the values of Median and Mode, we get

$\rm :\longmapsto\:29 = 3 \times 26 - 2Mean$

$\rm :\longmapsto\:29 = 78 - 2Mean$

$\rm :\longmapsto\:2Mean = 78 - 29$

$\rm :\longmapsto\:2Mean = 49$

$\bf\implies \:Mean = 24.5$

Additional Information :-

• The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

• The median is the middle value when a data set is ordered from least to greatest.

• The mode is the number that occurs most often in a data set.