Question

Type the correct answer in each box. Spell all words correctly and use numerals instead of words for numbers. If nessecary , use / for the fraction bar (s)

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 it’s value expressed up to one decimal place is ___

Answer 1

Answer : The best measure of center for this data set is the median and it’s value expressed up to one decimal place is 37.5

Step by step explanation :

We can determine the measure of center by three methods which are mean, mode, median. But the best measure of center for this data set is the median because it is most reliable when the data set is skewed or ordinal data.

For the calculation of the median, first we have to arrange the given set of data in ascending order.

The arranged set of data will be,

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

Formula used for median :

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

where, 'n' is the total number of observations.

The total number of observations, n = 14

Now put the value of n in the formula of median, we get

`Median=(((14)/(2))^(th)observ+((14)/(2)+1)^(th)observ)/(2)=(7^(th)observ+8^(th)observ)/(2)`

Now we have to calculate the 7th and 8th observation from the given set of data.

`7^(th)observ` = 37

`8^(th)observ` = 38

`Median=(37+38)/(2)=35.5`

Hence, the best measure of center for this data set is the median and it’s value expressed up to one decimal place is 37.5