3.1- Summaries For Symmetric Distributions

Question 1

Mean + typical value explained better

Answer 1

Use this to find out what’s typical (average)

For eyeballing mean- It is solid point that i can virtually balance whole graph on if my fingertip is at this point _ it will closely match the typical value (tallest bar) and if its symmetrical, center SHOULD be on the mean bar (IMPPP for comparing higher means-

just cuz one is more symmetric doesn’t mean it has higher mean- it’ll help you IDENTIFY it but if one has taller mean bar than they have higher mean)
SO if it’s NOT symmetrical, the bar next to the tallest is the mean
If it IS symmetric-> just use that ONE bar (mean is “left post number”)

Question 2

Standard deviation

Answer 2

With symmetrical data, we use mean to establish the typical value of the data (puts a number to our variability)
Measures How far away this typical value is from the mean (imp for analyzing which graphs have larger SDs- if their taller bars are farther away from the mean/ physical center)

You add every data value (x) (or input them individually in stat crunch) , then subtract mean from it (x-), then square that, THEN add it all up (epsilon) THEN divide by n-1 (n=total) THEN square root
On graph- literally the DIFFERENCE between the numbers on the tick marks
SD is meant for comparing VARIATION in data sets! So if SD number is higher in one group, their responses had most variation
* the more symmetrical your data is, smaller SD will be (less variation/ outliers)

Question 3

Stat crunch mean

Answer 3

Input ALL values in order (even 0)
You run Var1 (variable 1) in columns
Ex= mean
X-= added all up
Sx= standard deviation

Question 4

How we use SD/ measuring by SD

Answer 4

Explaining in context:
SD= 10.7 paid vacation days
On average these values vary from that mean (17.3) by 10.7 vacation days
On average these countries vary 10.7 paid vacation days from the mean
* kinda like measuring up values by their distance from mean card (above or below)

In a symmetric, unimodal graph-> 2/3s of observations will be WITHIN (less OR more, either one) one SD from the mean
* 2/3s of data is between ONE SD
- 17.3 (mean) + 10.7 (SD)= 28 <- ONE SD above the mean
- 17.3 MINUS 10.7 = 6.6 <- ONE SD below the mean
- SO 66% (2/3) of my data should be between 28 and 6.6 vacation days
* it’ll ask “find . . One SD above and below mean”

• shows the AVERAGE of how much ALL the values deviate, not just a few as in with the 99, 68, 97% rule

Question 5

What mean means

Answer 5

On average between the 6 countries, PEOPLE got 17.3 paid vacation days
All the values are regarded as being above or below this
Measure its distance away by this formula: value - mean
Mean= add up all/ # of all

• this all shows us the averages of data (summarizes) and how to measure individuals against it (above or below)

Question 6

SD tip

Answer 6

The x is where you plug in values
“Within one SD from mean” includes both LESS THAN and MORE THAN (value directly to left or mean and value directly to right)

Question 7

Comparing variation

Answer 7

The not like other girls thing is real- it’s about spread out Ness, yes, but if the HIGHER frequencies are away from the mean= more variation
1. With raw data- look for HOW SPREAD the number VALUES are (20-60 is more than 20-30)
2. Eyeball - biggest value- smallest but if their the SAME - doesn’t matter about biggest value- smallest, the number in between varying MATTER
*notice that it us usually won’t start at 0 it’s cuz these raw values are the FREQUENCIES. NOT the x -axis SDs, but the frequency SDs (particularly for this raw data only)
3. When they have the same mean, maximum and minimum, it’s about distance of the ADJACENT TWO numbers from the mean