Question

Whats the answer

The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.

{36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}

The best measure of center for this data set is the , and its value expressed up to one decimal place is
Mathematics

Answer 1

Median

Explanation:

The given data set is:

36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29

The best measure of center for the given data will be median as median is the central value of the given data set which represents the center.

Thus, in order to find the median, first arrange the given data set in ascending order, we have

16, 18, 28, 29, 35, 36, 37, 38, 40, 41, 44, 66, 68, 72

Now, the median is given as:

`M=(37+38)/(2)`

`M=(75)/(2)`

`M=37.5`

Therefore, the value of median is 37.5

Answer 2

The best measure of center for this data set is the median, and its value expressed up to one decimal place is 37.5.

Explanation:

Given : The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.

{36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}

To find : The best measure of center for this data set and its value expressed up to one decimal place?

Solution :

Arrange in ascending order

{16,18,28,29,35,36,37,38,40,41,44,66,68,72}

First we find the mean and median of the data

Mean is defined as
`M=(\sum x)/(n)`

`M=(16 + 18 + 28 + 29 + 35 + 36 + 37 + 38 + 40 + 41 + 44 + 66 + 68 + 72)/(14)`

`M=(568)/(14)`

`M=40.57`

Mean of the data set is 40.57.

Median is defined as average of two middle term

`m=(7th+8th)/(2)`

`m=(37+38)/(2)`

`m=(75)/(2)`

`m=37.5`

Median of the data set is 37.5.

Range of the set is 72-16=56

Mean is not appropriate as the range is very high so the best measure is median.

Therefore, The best measure of center for this data set is the median, and its value expressed up to one decimal place is 37.5.