Respuesta :
Answer:
The best measure of center is median = 37.50.
Step-by-step explanation:
The complete question is:
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?
Solution:
The three measures of center are:
- Mean
- Median
- Mode
The mean is the average value of the data set and uses all the values of the data set.
The median is the middle value of the data set.
Mode is the value of the data st with the highest frequency or number of occurrence.
Compute the mean, median and mode of the data set provided as follows:
[tex]\text{Mean}=\frac{1}{n}\sum X=\frac{1}{14}\times [36+18+....+72+29]=40.57[/tex]
So, the mean is 40.57.
The data set in ascending order is:
{16 , 18 , 28 , 29 , 35 , 36 , 37 , 38 , 40 , 41 , 44 , 66 , 68 , 72}
There are 14 values in the data set. That is an even data set.
The median for an even data set is the average of the middle two values.
The middle two values are: 37 , 38
Average of {37 , 38} = [tex]\frac{37+38}{2}=37.50[/tex]
So, the median is 37.50.
None of the values are repeating itself. Thus, the data does not have a mode.
For the provided data:
Mean > Median
Implying that the data set is right-skewed.
For a skewed distribution or data set the median is the measure of center.
Thus, the best measure of center is median = 37.50.
