Question

6. Raw Data: 3,5,7,4,3, 8, 6, 6,9, 6,7,8,9,3, 3, 9 There are 16 data items Find: a) Mean b) Median c) Midrange d) Mode 7. Find the standard deviation of the data in question 6

Answer 1

6.a. Mean= 6

b. Median=6

c Midrange=6

d.Mode=4

7.Standard deviation=2.2079

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=
`(sum\;of\;data\;items)/(total\;data\;items)`

Mean=
`(96)/(16)`

Mean=6

b.If total number of items are even then

Median=
`((n)/(2)^(th)\;observation+\left((n)/(2)+1\right)^(th))/(2)`

Median=
`((16)/(2)^(th) observation+\left((16)/(2)+1\right)^(th) observation)/(2)`

Median=
`(8^(th) observation+9^(th) observation)/(2)`

Median=
`(6+6)/(2)`

Median=
`(12)/(2)`

Median=6

c. Midrange=
`(lower\;value+highest\;value)/(2)`

Lower data item=3

Highest data item=9

Midrange=
`(3+9)/(2)`

Midrange= 6

d.Mode : It is defines as a number that appear most often in a set of numbers.

Mode=3

7. Mean
`\bar x=6`

`\mid x-\bar x\mid`
`{\mid x-\bar x\mid}^2`

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

`\sum{\mid x-\bar x\mid}^2=78`

n=16

Standard deviation=
`\sqrt{\frac{\sum{\mid x-\bar x}^2}{n}}`

Standard devaition=
`\sqrt{(78)/(16)}`

Standard deviation=
`√(4.875)`

Standard deviation of data =2.2079