9.6_Linear Transformation of data

Adding or subtracting a value to all the observations in a data set will increase each of the following by that amount, except for this one...

• mean

• median

• quartiles

• IQR

Multiplying or dividing all the observations in a data set by the same amount will affect which of the measures below?

• mean

• standard deviation

• mode

• range

• all of the above

Suppose the weekly earnings of 7 Dunkin' Donuts employees are:

$40, $46, $47, $48, $50, $50, $53

The Range of these weekly earnings is $13.

If each worker is given a $25 bonus, what is the new range?

• $25

• $38

• $13

• $12

During her time on Dancing with the Stars, Carole Baskin received the following scores:

11, 16, 12.

The standard deviation of her scores is 2.16. If Carole was able to add 3 points to each of her scores, what would the new standard deviation be?

• The standard Deviation would remain the same (Sorry Carole)

• 3

• 5.646

• 7.938

Suppose we asked 9 people how many Bernie memes they saw yesterday and the response was (# of memes):

10, 12, 12, 13, 14, 15, 18, 19, 22

The IQR of this data is 6.5. If each of these numbers are doubled, what will the new IQR be?

• IQR=6.5

• IQR=8.5

• IQR=13

• IQR=15

Suppose your data set is

1, 1, 2, 3, 5, 8, 9

The median for this data set is 3. Find the new median if each term is multiplied by 3.

• 3

• 9

• 7

• 6

Suppose we have the following data set:

5, 14, 9, 9, 6, 3, 0, 9, 3

With a mode = 9. If we multiply each number in our set by 2, what will the new mode be?

• 9

• 3

• 6

• 18

TRUE OR FALSE:

If you add a constant to a data set, you have to add that constant to the mean, median, mode, quartiles, and all the numbers in the data set.

• True

• False

TRUE OR FALSE:

When adding a constant to a data set, you have to add that constant to the range, IQR, and standard deviation.

• True

• False

TRUE OR FALSE:

When multiplying a data set by a constant, you only multiply the range, IQR, and standard deviation by that constant.

• True

• False