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

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.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°