Question

median and mode. plz plz ​

Answer 1

$\textbf{\underline{Answer :- }}$

$\textbf{\underline{Explanation :-}}$

$\textbf{\underline{Mode}}$

The number with highest frequency.

Numbers = 71 , 75 , 85 , 64 , 80 , 71 , 75 , 75 , 78, 76 , 88 , 79 , 86 , 75.

$\textsf{\underline{Table =}}$

$\begin{tabular}{|c|c|}\cline{1-2} Number & Frequency\\\cline{1-2}\ 64 & 1\\\cline{1-2}\ 71 & 2\\\cline{1-2}\ 75&4\\\cline{1-2}\ 76&1\\\cline{1-2}\ 78&1\\\cline{1-2}\ 79&1\\\cline{1-2}\ 80&1\\\cline{1-2}\ 85&1\\\cline{1-2}\ 86&1\\\cline{1-2}\ 88&1\\\cline{1-2}\end{tabular}$

As Given above the highest frequency is of number 75 with 4 as frequency.

$\therefore$The mode of the Given data is 75.

$\textbf{\underline{Median}}$

The the central observation is the median of the given data.

To find the Median we need to arrange the data in Ascending or Descending order.

$\textsf{\underline{Ascending order :-}}$

64 < 71 < 75 < 76 < 78 < 79 < 80 < 85 < 86 < 88

As the observations are even, there are two Central observations = 78 and 79

When there even number of observations we need to find the average of the central observations.

$\textsf{\underline{Median :}}$

$\tt{\implies \dfrac{78 + 79}{2} }$

$\tt{\implies \dfrac{157}{2} }$

$\tt{\implies \: 78.5}$

$\therefore$The Median of the given data is 78.5

$\textbf{\underline{Mode = 75}}$

$\textbf{\underline{Median = 78.5}}$