Question

What is the mean, median and mode of \[68,74,71,69,74,78,70\]?

Answer 1

Hint: In order to find the mean of the given observations, we can find the mean by adding all the observations and then dividing the result by the number of observations. In order to find the median, firstly, we have to arrange the given observations in the ascending order or descending order and then we have to find the middle most observations of the given observations. The mode can be calculated by finding the most repeated observation.

Complete step by step solution:
Now let us learn more about the mean, median and mode. The mean can be found by the formula \[\overset{-}{\mathop{x}}\,=\dfrac{\text{sum of observations}}{\text{number of observations}}\]for a raw data. Raw data is nothing but the data collected directly and noted. If the number of given observations of raw data is even, then the median can be found by the average of the middle terms of the observations. A set of data can have one mode or no mode or more than one mode.
Now let us find out the mean of the given data.
The given observations are \[68,74,71,69,74,78,70\].
By applying the formula \[\overset{-}{\mathop{x}}\,=\dfrac{\text{sum of observations}}{\text{number of observations}}\]
We get, \[\overset{-}{\mathop{x}}\,=\dfrac{68+74+71+69+74+78+70}{7}\]
Upon solving this, we obtain
\[\begin{align}
  & \overset{-}{\mathop{x}}\,=\dfrac{504}{7} \\
 & \overset{-}{\mathop{x}}\,=72 \\
\end{align}\]
\[\therefore \] The mean is \[72\].
Now let us calculate the median of the given data.
Firstly, let us arrange the given data in ascending order.
\[68,69,70,71,74,74,78\]
The number of observations is \[7\], so the middle most term would be \[{{4}^{th}}\] term.
The \[{{4}^{th}}\] term in the data is \[71\].
\[\therefore \] The median is \[71\].
Now we will be calculating the mode of the observations of the data.
Mode is the most frequently occurring data.
From the data the most frequently occurred data is \[74\] since it has repeated twice and all other observations only once.
\[\therefore \] The mode is \[74\].

\[\therefore \] The mean, median and mode of \[68,74,71,69,74,78,70\] is \[72,71,74\] respectively.

Note:
Mean, median and mode are together called as the measures of the central tendency. If the data has two modes, then it is called bimodal data. By comparing the median to the median, we get the idea of the distribution in the data.