Question

A population of a rare species of beetle consists of seven individuals whose masses in grams are shown below. What is the approximate value of the variance?

3,6,5,8,4,2,7

A. 2
B. 2.16
C. 4
D. 5

Answer 1

ugh standard deviation :O
find the standard deviation then square that to find the variance

Answer 2

I think its C

Answer 3

to find the standard deviation get the average of the numbers then you can now solve for the variance by getting the average of their square then subtract it by the square of what you get in standard deviation
@joshguy22 I hope it will help xD

Answer 4

The population standard deviation is 2. Therefore the variance is\[\sigma ^{2}=2^{2}=4\]

Answer 5

@kropot72
why did you use 2 ??? xD

Answer 6

I entered the data in ascientific calculator and used the sigma x function to find the population standard deviation. The result was 2. This must be squared to find the variance. How did you arrive at 4 for the variance?

Answer 7

to get the variance

first find the standard deviation get the average of the numbers then you can now solve for the variance by getting the average of their square then subtract it by the square of what you get in standard deviation
\[(3+6+5+8+4+2+7)/ 7= 5\] standard deviation

to get the variance square the number divide by its total w/c is 7
then subtract to the square of standard deviation
@kropot72
I see I will try it using my calculator
ty XD

Answer 8

The variance can be calculated directly as follows:
Let X = an individual value
Let X bar = the average of the individual values.
The variance, sigma squared, is found from:\[\sigma ^{2}=\frac{\Sigma[(X-Xbar)^{2}]}{n}\]
In this case X bar = 35/7 = 5
The deviations from X bar are -2, +1, 0, +3, -1, -3, +2.
Squares of the deviations are 4, 1, 0, 9, 1, 9, 4
the mean square deviation (or variance) =
\[\frac{4 + 1 + 0 + 9 + 1 + 9 + 4}{7}=4\]

Answer 9

@kropot72
I try to use my calculator but I dont know what will i input

Answer 10

Does your calculator have a statistics function? If it does your should be able to enter the individual data values using the DATA key.

Answer 11

http://en.wikipedia.org/wiki/Variance#Discrete_random_variable

Answer 12

\[\Large =\sum_{n=2}^{8} \frac 17 \left( n-5 \right)^2=\frac27\left( 3^2+2^2+1^2 \right)=\frac 27\times 14 \]

=4