Mathematics, 13.10.2020 03:01 AquariusOx

Select all of the true statements about the standard deviation of a quantitative variable. 1. Standard deviation is resistive to unusual values. 2.The standard deviation of a set of values is equal to 0 if and only if all of the values are the same. 3. Standard deviation is never negative. 4.Changing the units of a set of values (e. g., converting from inches to feet) does not affect its standard deviation. 5.If a set of values has a mean of 0 and a standard deviation that is not 0, then adding a new data point with a value of 0 will have no effect on the standard deviation. 6.Standard deviation represents how far a group of values are from the mean of those values, on average.

Answers: 1

Show answers

Answers

Answer from: petroale000

Considering the first statement

Standard deviation is resistive to unusual values

This statement is false because standard deviation is the numeric measure of deviation of the each observation from the mean

Considering the second statement

The standard deviation of a set of values is equal to 0 if and only if all of the values are the same.

This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.

Considering the third statement

Standard deviation is never negative.

This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.

Considering the fourth statement

Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation

This statement is false because standard deviation is the numeric measure of deviation of the each observation from the mean

Considering the fifth statement

If a set of values has a mean of 0 and a standard deviation that is not 0, then adding a new data point with a value of 0 will have no effect on the standard deviation.

This statement is false because , let take an example

x -4 - 3 0 3 4

Generally the mean is mathematically evaluated as

$\= x = \frac{\sum x_i }{n}$

=> $\= x = \frac{-4+ (- 3)+ 0 + 3 + 4 }{5}$

=> $\= x = 0$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x_ i - \= x )^2}{y} }$

$\sigma = \sqrt{\frac{ (-4 - 0 )^2 + (- 3 - 0 )^2 + (0 - 0 )^2 + (3 - 0)^2 + (4 - 0 )^2}{5} }$

=> $\sigma = 3.16$

Now when zero is removed the standard deviation is

$\sigma_1 = \sqrt{\frac{ (-4 - 0 )^2 + (- 3 - 0 )^2 + (3 - 0)^2 + (4 - 0 )^2}{4} }$

=> $\sigma_1 = 3.54$

Since $\sigma \ne \sigma _1$ the above statement is false

Considering the sixth statement

Standard deviation represents how far a group of values are from the mean of those values, on average.

This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.

Step-by-step explanation:

Answer from: Quest

answer:

c. the third graph

Answer from: Quest

$3 \times 4 = 12 \\ 6 \times 8 = 48$ $48 + 12 = 60$ hope it is correct if not i'm srry i tried to

Questions in other subjects:

Computers and Technology, 09.10.2019 20:00

Suppose that a cashier owes a customer some change and that the cashier only has quarters, dimes, nickels, and pennies. write a function that computes the minimum number of coins t...

Mathematics, 09.10.2019 20:00

At a given level of effort, it is reasonable to assume that the rate at which fish are caught depends on the population y: the more fish there are, the easier it is to catch them....

Business, 09.10.2019 20:00

The following income statement data (in millions) for dunn inc. and heston company were taken from their recent annual reports: 1 dunn heston 2 net sales $63,000.00 $115,000.00 3...

Business, 09.10.2019 20:00

John den bear company had a $150,000 beginning balance in accounts receivable and a $6,000 credit balance in the allowance for doubtful accounts. during the year, credit sales were...

Business, 09.10.2019 20:00

During 2021, lebron corporation accepts the following notes receivable. on april 1, lebron provides services to a customer on account. the customer signs a four-month, 9% note for...

Business, 09.10.2019 20:00

Consider the following simplified financial statements for the yoo corporation (assuming no income taxes): income statement balance sheet sales $ 30,900 assets $ 25,450 debt $ 6,9...

Mathematics, 09.10.2019 20:00

The mean number of daily surgeries at a local hospital is 6.2. assume that surgeries are random, independent events. (a) the count of daily surgeries follows approximately: a pois...

Computers and Technology, 09.10.2019 20:00

For order # 1001, find productid, orderedquantity, productstandardprice, and the total price (orderedquantity x productstandardprice) for each product item involved in this order...

Arts, 09.10.2019 20:00

With the introduction of rock and roll dance forms and performers, dancers began to include what aspect into their social dance? a. elaborate floor patterns b. movin...

Computers and Technology, 09.10.2019 20:00

Display orderid, productid, orderdate and ordered quantity for orders made after october 23, 2010, with at least four units for a product...

More questions: Mathematics Another questions

Answers

Other questions on the subject: Mathematics

Questions in other subjects: