Question

For which data representation is the median the better measure of center

Answer 1

We know that
The Median is the "middle" of a sorted list of numbers.
To find the Median, place the numbers in value order and find the middle

case a) the data is 
3,8,4,8,3
place the numbers in value order-----> 3,3,4,8,8

the middle is 4
so
the median is 4


case b) the data is 
2,2,3,5,5
place the numbers in value order-----> 2,2,3,5,5  

the middle is 3
so
the median is 3

case c) the data is 
6,2,6,2,6
place the numbers in value order-----> 2,2,6,6,6

the middle is 6
so
the median is 6

case d) the data is 
1,3,4,3,1
place the numbers in value order----->1,1,3,3,4

the middle is 3
so
the median is 3


we know that
The Mean is most often chosen when the data is continuous and symmetrical (normal). ------> case a) case c) and case d) If the data has outliers or is skewed, then the mean would paint a skewed view of centrality

The Median is especially useful with skewed distributions as it draws the line right in the middle of your data set------> case b)

therefore

the answer is
case b) 

Answer 2

Answer with explanation:

Mean is sum of all the observation divided by total number of observation, where as median is middlemost observation of the data set, while mode is most occurring variate or data value in the data set.

1. Variate or Data set which is represented in Histogram is

 3,8,4,8,3

Arranging it in ascending order, we get

3,3,4,8,8

Data is skewed right.So, Mean >Median>Mode

Mean =5.2

Number of observation is 5. So,Median will be Middle term,that is third term equal to 4.

Mode =3 or ,8 which will be equal to 3,as data is skewed right.

→Mean gives better representation of data set,because, 5.2-3=2.2 and, 8-5.2=2.8

2. Variate or Data set which is represented through dots is

 2, 2, 3,5,5

Arranging it in ascending order, we get

2,2,3,5,5

Data is skewed right.So, Mean >Median>Mode

Mean=3.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =2 or 5 which will be equal to 2,as data is skewed right.

→Mean gives better representation of data set,because, 3.4-2=1.4 and, 5-3.4=1.6

3. Variate or Data set which is represented in Histogram is

 6,2,6,2,6

Arranging it in ascending order, we get

2,2,6,6,6

Data is skewed left.So, Mean <Median<Mode

Mean=4.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 6.

Mode =6

→Mode gives better representation of data set.

4.Variate or Data set which is represented through dots is

 1,3,4,3,1

Arranging it in ascending order, we get

1,1,3,3,4

Data is skewed left.So, Mean <Median<Mode

Mean=2.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =1 or 3,data is skewed left,so mode =3

Here, in this data set, both mode and median are better measure of center than Mean,as there are two modes in the data set, so choosing median as measure of center,because data is skewed left,

For ,Option 4: Median is the better measure of center.