3.2 Empirical Rule And Z Scores

Question 1

Empirical rule

Answer 1

Measures 1 to 3 SDs from mean
1 SD- 68% of data (2/3s)
But really on either side of the mean , one SD is 34% of the 50% that divide the graph (mean divides by 50%)
34% + 34% = 68%
2 SDs- 95%
3 SDs- 99.7%

• we can have this SET rule with means because although they are sensitive, they still maintain this consistency of data being related (whether it be above or below) a set mean, even if that mean has been affected by an outlier, it is still the mean and thereby WHEREVER it is, has this rule affecting the whole graph

Question 2

Unusual value s

Answer 2

If the z score (which is the DIFFERENCE away/between the SDs in context of empirical rule SDs, not actual SD value given with mean) is More OR LESS than 2 SDs away from mean

So distance away from mean, but not technical tick marks like SDs are directly away from the mean (z score doesn’t have to land on tick mark)

Question 3

Z scores (w/o formula)

Answer 3

Basically asking how many SDs a value is away from mean (above or below)
Like the empirical rule percentages except we use this to LITERALLy identify the values WITHIN those ranges
Will ask for number value - they give SD number (at -3 SD)
Go DOWN 3 tick marks from the mean

will ask for SD distance away (-3) - they give a value (what is z-score for a CHILD that got 115) - notice a z score is for a person/ the variable/ country
Locate value on tick mark, count how many tick marks it takes to get to mean (can be positive or negative number)
!!!!!1
* if value isn’t EXACTLY on tick mark-> value/ SD (or z score formula )

Question 4

Identifying the SDs that disguise NVs

Answer 4

(Making SD values for tick marks)
can be from adding SD from the mean but that works best for starting at 1, if they want you to find the THIRD SD value: mean plus or minus 3(SD)

Question 5

Tip

Answer 5

The numbers on ticks are SDs so they are generalizations and don’t represent the ACTUAL raw data NVs, this is all measuring and seeing what ranges are normal compared to AVERAGED concepts

Question 6

Z score Formula

Answer 6

(Other card pretty much)
“How many SDs is that?” Is what z score rlly asks for -> take diff between mean and value (x), then see how many SDs fit in this difference ->
X-(x-) <- distance from mean
———
SD <- how many SDs can first in that distance

Question 7

What to do with z scores

Answer 7

Compare them on the basis of their tendency to be more or less UNUSUAL. (Remember 2 SDs awaY!!!)
If one is closer to their mean than the other they are LESS unusual so they win

Question 8

Confusion about unusual SDs

Answer 8

!!!! Think about it like its a number line (smaller values on left and the values go up in size as they go right)

Question 9

How many standard deviations is the SD away from the SD

Answer 9

SD asked about
——————
SD in context

Question 10

Reminder

Answer 10

Z scores can be negative

Question 11

Value to be considered common

Answer 11

Relatively close to its mean (which z score is closer to zero)