Question

Find the mean ,median and mode of the weights of people shown

Answer 1

`(a)\ Mean = 80kg`

`(b)\ Median = 76kg`

`(c)\ Mode = 61kg`

Explanation:

Given

`Data:105kg, 53kg ,76kg ,91kg ,120kg ,61kg ,55kg ,98kg ,61kg`

`n = 9`

Solving (a): The mean

This is calculated using:

`\bar x = (\sum x)/(n)`

`\bar x = (105kg+53kg +76kg +91kg +120kg +61kg +55kg +98kg +61kg)/(9)`

`\bar x = (720kg)/(9)`

`\bar x = 80kg`

Hence:

`Mean = 80kg`

Solving (b): The median

`Data:105kg, 53kg ,76kg ,91kg ,120kg ,61kg ,55kg ,98kg ,61kg`

Arrange in ascending order

`Data: 53kg ,55kg, 61kg ,61kg,76kg ,91kg ,98kg , 105kg,120kg`

`n = 9`

So, the position of the median element is:

`Median = (n+1)/(2)th`

`Median = (9+1)/(2)th`

`Median = (10)/(2)th`

`Median = 5th`

The 5th element is 76kg

Hence:

`Median = 76kg`

Solving (c): The mode

In the given data

`Mode = 61kg`

Because it has a frequency of 2 (the highest), others have 1