Question

Find the mean median and mode for the following data 15 17 16 14 17 16 11 15 17 14

Answer 1

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Q1) Find the mean, median, and mode for the following data 15,17,16,14,17,16,11,15,17,14

$\underline{\underline{{\purple{\sf Given}}}}$

$\odot\displaystyle\bf{15,17,16,14,17,16,11,15,17,14 \: ......given \: observation }$

$\divideontimes\boxed{\sf{ \: To\: Find \to \: Mean, Median, Mode }}$

$\\ \bullet\bf{Mean=\dfrac{Sum\: of \: the \: Observation }{Total\: Observation }}$

$\\ \dashrightarrow\displaystyle\tt{Mean=\dfrac{X_1+x_2+x_3+x_4......x_n}{n}}$

$\\ \dashrightarrow\displaystyle\tt{Mean=\dfrac{15+17+16+14+17+16+11+15+17+14}{10}}$

$\\ \dashrightarrow\displaystyle\tt{Mean=\dfrac{32+47+27+32+14}{10}}$

$\\ \dashrightarrow\displaystyle\tt{Mean=\dfrac{79+59+14}{10}}$

$\\ \dashrightarrow\displaystyle\tt{Mean=\dfrac{79+73}{10}}$

$\\ \dashrightarrow\displaystyle\tt{Mean=\dfrac{152}{10}}$

$\\ \dashrightarrow\displaystyle\tt{Mean=\cancel\dfrac{152}{10}=15.2}$

$:\implies\underline{\boxed{\sf{Mean=15.2}}}$

$\divideontimes\underline{\boxed{\bf{Median=\dfrac{n_1+n_2}{2}}}}$

✪Median ::

$\: \\ \implies\bf{median = \frac{17 + 16}{2} = \frac{33}{2} = 16.5}$

$\underline{\boxed{\tt{Median=16.5}}}$

$\divideontimes\displaystyle\bf{Mode\to \: Maximum \: Observation \: of \: series}$

✯Mode::

(1)15 ➟2observation

(2) 17 ➟3observation

(3) 16➟2observation

(4) 14➟2observation

(5) 11➟1 observation

$\implies\displaystyle\bf{Maximum\: observation \to \: 17}$

$\bigstar\underline{\boxed{\tt{mean=15.2\: and\: median =16.5\: and\: mode=17}}}$

Answer 2

Step-by-step explanation:

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