Question

If the heights of 5 people are 144cm, 152cm, 151cm, 158cm and 155cm respectively. Find the mean height.

Answer 1

Hint: We know that mean or arithmetic mean is the most commonly used form of average. To find the mean of a quantity \[{{x}_{1}},{{x}_{2}},{{x}_{3}}............{{x}_{n}}\] is given by as follows:
\[\bar{x}=\text{mean=}\dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+............{{x}_{n}}}{n}\]
So, we will use the above formula to find the required mean.

Complete step-by-step answer:
We have been given the height of 5 people as 144cm, 152cm, 151cm, 158cm and 155cm respectively and we have to find the mean height.
We know that, mean is the sum of all values in the data set divided by the number of values in the data set. If we have the values \[{{x}_{1}},{{x}_{2}},{{x}_{3}}............{{x}_{n}}\] in a data, then, mean is given by,
\[\bar{x}=\dfrac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+............{{x}_{n}}}{n}\]
Now, we have all the values and also the total number of values is also known to us. Therefore, we can substitute the values in the above equation and we will get,
\[\begin{align}
  & \Rightarrow \text{mean height=}\dfrac{144+152+151+158+155}{5} \\
 & \Rightarrow \text{mean height=}\dfrac{760}{5} \\
 & \Rightarrow \text{mean height=} 152cm \\
\end{align}\]
Hence, we have obtained the mean height of 152cm.

Note: Remember the fact about mean is that, mean is the average of the values in a data. It can be calculated by taking a sum of all the values and then dividing it by number of values. Also, in statistics, it is the most common method to measure the center of a data set. Sometimes, by seeing five values, students directly write the mean as the third term, i.e. 151 cm as the answer. But, this is not valid. The set of values must be in ascending order, i.e. 144, 151, 152, 155 and 158. Then, we can say that the third term will be the mean.