Question

Which set of numbers has the largest variance?

Answer 1

Answer:

1) (1,3,4.7)

2) 6.8

3) the square root of the variance

4) has the same units as the underlying data

5) It has predictive power.

Step-by-step explanation:

From question one, it is possible to use an excel formula to calculate the variance of the set of numbers.

Now, to calculate the variance in an Excel sheet:

Make sure your data is in a single range of cells in Excel.  

If your data represents the entire population, enter the formula as "=VAR. P(A1:A4). Since, we were given four variables  

The variance for your data will be displayed in the cell.  

i.e for set of numbers (7, 8, 9, 10)

variance = (VAR. P(A1:A4))

= 1.25

for set of numbers (1, 3, 4, 7)

variance = (VAR. P(A1:A4))

= 4.69

for set of numbers (4,2,1, 0)

variance = (VAR. P(A1:A4))

= 2.19

for set of numbers (1, 0, 2, 4)

variance = (VAR. P(A1:A4))

= 2.19

The set of numbers (1,3,4.7) indicates the largest variance from the foregoing.

2) What is the population variance of the following set of numbers: 3, 5, 8, 9, 10?  

Using the same method explained in question 1, the population variance of the following set of numbers 3,5,8,9,10 can be calculated as:

For the set of numbers (3, 5, 8, 9, 10)

Variance = (VAR. P(A1:A5)) since it contains five sets.

= 6.8

3) Variance can be defined as the average of the squared differences from the Mean. Therefore, Standard deviation is the square root of the variance which is given as:

$S= \sqrt{\frac{E^N_i(x_i-x)}{N-1} }$

where;

s = sample standard deviation

N = the number of observations

$x_i$ = the observed values of a sample item.

x= the mean value of the observations

4) Standard deviation is useful because it has the same units as the underlying data

5)  Of all the characteristics of Standard deviation when relating to finance,  Standard deviation  do not possess  predictive power.