Question

Use the given graph to find the mean, median and mode of the distribution:

Answer 1

The data set for the given distribution is,

`\mleft\lbrace6,6,6,7,7,7,7,8,8,8,9,9,9,9,10,10,10,10,10,10\mright\rbrace`

Determine the sum of data set.

`\begin{gathered} \text{Sum}=6\cdot3+7\cdot4+8\cdot3+9\cdot4+10\cdot6 \\ =18+28+24+36+60 \\ =166 \end{gathered}`

The number of observaions in the data set is 20.

Determine the mean for the given distribution.

`\begin{gathered} \text{Mean}=(166)/(20) \\ =8.3 \end{gathered}`

So mean is 8.3.

There are 20 terms in data set. So median value is average of (20/2)th term and (20/2 + 1) term.

The 10th term is 8 and 11th term is 9.

Determine the average of 10th and 11th term.

`\begin{gathered} \text{Median}=(8+9)/(2) \\ =(17)/(2) \\ =8.5 \end{gathered}`

So median of data set is 8.5.

The frequency of number 10 is 6, which is highest as compare to other number. So mode of distribution is 10.

So mode is 10.