Answer:
6.a. Mean= 6
b. Median=6
c Midrange=6
d.Mode=4
7.Standard deviation=2.2079
Step-by-step explanation:
Given data
3,3,3,3,4,5,6,6,6,7,7,8,8,9,9,9
Total data items,n=16
Sum o data items=96
a. Mean=[tex]\frac{sum\;of\;data\;items}{total\;data\;items}[/tex]
Mean=[tex]\frac{96}{16}[/tex]
Mean=6
b.If total number of items are even then
Median=[tex]\frac{\frac{n}{2}^{th}\;observation+\left(\frac{n}{2}+1\right)^{th}}{2}[/tex]
Median=[tex]\frac{\frac{16}{2}^{th} observation+\left(\frac{16}{2}+1\right)^{th} observation}{2}[/tex]
Median=[tex]\frac{8^{th} observation+9^{th} observation}{2}[/tex]
Median= [tex]\frac{6+6}{2}[/tex]
Median= [tex]\frac{12}{2}[/tex]
Median=6
c. Midrange=[tex]\frac{lower\;value+highest\;value}{2}[/tex]
Lower data item=3
Highest data item=9
Midrange= [tex]\frac{3+9}{2}[/tex]
Midrange= 6
d.Mode : It is defines as a number that appear most often in a set of numbers.
Mode=3
7. Mean[tex]\bar x=6[/tex]
[tex]\mid x-\bar x\mid[/tex] [tex]{\mid x-\bar x\mid}^2[/tex]
3 9
3 9
3 9
3 9
2 4
1 1
0 0
0 0
0 0
1 1
1 1
2 4
2 4
3 9
3 9
3 9
[tex]\sum{\mid x-\bar x\mid}^2=78[/tex]
n=16
Standard deviation=[tex]\sqrt{\frac{\sum{\mid x-\bar x}^2}{n}}[/tex]
Standard devaition=[tex]\sqrt{\frac{78}{16}}[/tex]
Standard deviation=[tex]\sqrt{4.875}[/tex]
Standard deviation of data =2.2079
