Question

How can I determine the mean value ? How do I calculate the median of the distribution?

Answer 1

In general, the mean value of a histogram is given by the formula below

`\begin{gathered} mean=\sum_i(m_in_i)/(N) \\ m_i\rightarrow\text{ midpoint of the ith interval} \\ n_i\rightarrow\text{ frequency of the ith interval} \\ N\rightarrow\text{ Total sample size} \end{gathered}`

Thus, in our case,

Therefore, the mean value is 134cm

As for the median of a histogram, order the values of the data set from least to greatest, as shown below

`\begin{gathered} 1st,1st,1st,2nd,2nd,...,3rd,3rd,...,7th,7th,8th,8th \\ Where \\ 1st\rightarrow indicates\text{ an element in the first interval \lparen100-109\rparen} \\ 2nd\rightarrow\text{ indicates an element in the second interval \lparen110-119\rparen} \\ ... \end{gathered}`

Thus, the median of the distribution is

`\begin{gathered} 3+7+13+20+7+6+2+2=60 \\ \Rightarrow median=\frac{29th\text{ }value+30th\text{ }value}{2}=130-139\text{ class} \end{gathered}`

Therefore, the median of the data set is the interval 130-139 cm