Question

6 Points possible: 3. Total attempts: 5

For the data shown, answer the questions. Round to 2 decimal places.


x


7.3


11.7


21.7


18.8


23.2


20.7


29.7


21.2


10.6




Find the mean:


Find the median:


Find the standard deviation:

Answer 1

Mean=18.32

Median=20.7

Standard deviation=7.10

Explanation:

Mean is the average of the sample size. It is calculated by dividing the sum of all the observations by the number of observations.

`mean=(7.3+11.7+21.7+18.8+23.2+20.7+21.2+10.6)/(9)`

`\Rightarrow mean=18.32`

Median is the middle value of the observations if the number of observations is odd. If the number of the observations is even then it is the middle value and the next observations average. The values need to be arranged in ascending order.

Therefore the observations become

`7.3, 10.6, 11.7, 18.8, 20.7, 21.2, 21.7, 23.2, 29.7`

In this case the number of observations is 9 which is odd

Therefore, the median is 20.7 i.e., the fifth observation

`Standard\ deviation=\sqrt \frac{\sum_(i=1)^(N)\left ( x_(i)-\bar{x} \right )^2}{N-1}`

`where,\ N=Number\ of\ observations\\\bar x=mean\\x_(i)=x_(1)+x_(2)+x_(3)+x_(4).........x_(N)`

`\left ({x_(i)}-\bar {x}\right )}^2`

`\\121.49\\43.85\\11.41\\0.23\\23.79\\5.65\\129.45\\8.28\\59.63\\\sum_(i=1)^(N)\left ({x_(i)}-\bar {x}\right )}^2=403.80\\N-1=9-1\\=8\\\therefore Standard\ deviation=\sqrt {(403.80)/(8)}=7.10`

Standard deviation=7.10