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

1 thought on “The median and mode respectively of a frecuenc<br />distribution are 26 and 29. Then find its mean​”

1. [tex]\begin{gathered}\begin{gathered}\bf \:Given – \begin{cases} &\sf{Median = 26} \\ &\sf{Mode = 29} \end{cases}\end{gathered}\end{gathered}[/tex]

   [tex]\begin{gathered}\begin{gathered}\bf \:To\:find-\begin{cases} &\sf{Mean} \end{cases}\end{gathered}\end{gathered}[/tex]

   [tex]\large\underline{\sf{Solution-}}[/tex]

   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

   [tex]\rm :\longmapsto\:Mode = 3Median – 2Mean[/tex]

   On substituting the values of Median and Mode, we get

   [tex]\rm :\longmapsto\:29 = 3 \times 26 – 2Mean[/tex]

   [tex]\rm :\longmapsto\:29 = 78 – 2Mean[/tex]

   [tex]\rm :\longmapsto\:2Mean = 78 – 29[/tex]

   [tex]\rm :\longmapsto\:2Mean = 49[/tex]

   [tex]\bf\implies \:Mean = 24.5[/tex]

   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.

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