2.1, 2.2 Visualizing Numerical Data

Question 1

UD

Answer 1

It doesnt have CVs, rather it’s one graph for ONE of the NV headers (its values and frequencies)
No other variables to compare it with (correlational), just observing the variability within itself (descriptive research)- the WHAT
Organize through different patterns of sample for better visualization + conclusion

• dot plots, histograms, stemplots
• summarize: shape- symmetry?
  Center- most common value?
  Spread- any data values farther from the rest?

Question 2

Analyze distributions (dot plot)

Answer 2

CHECK what each dot represents
Questions will center around the observation of the numerical values- patterns, density (popular values)
EX: what percentage are at least 68 mm?- researcher wants the amount of sampled measurements thats in that range (maybe its useful for their TOI)
Just because there is more dots on one value than teh rest- watch out for high but sparsed out variability outside fo that, because they accumulate in comparison to the obvious one
To accurately determine : obvious dots/ total dots
On dot plots it shows each person or each country aligning with whichever numerical variable they fall under (18 or 20)/ are a value of

Question 3

Categories

Answer 3

We are looking at numerical distributions of the numerical variable for a conclusion of TOI

You cant put categories on a dot plot, but DO put categories underneath or beside the graph

Question 4

Outlier

Answer 4

Not like other dots

Question 5

Find true (not obvious) mode

Answer 5

Similar to dot plot card
1. Count dots of inquired numerical variable (age 18- dots)
2. Divide by total dots (all students on each age category)
3. Smaller than 0.5%? NOT MODE

Question 6

Relative frequency

Answer 6

Proportion in DECI form - frequency/ total
Proportion of the observations that exhibit the relevant characteristic (<- numerical variable)
Shown on frequency table (IMP- this frequency table has NUMERICAL HEADERS) - standard deviations too
Shows how FREQUENTly each numerical value shows up on a graph
Frequency-> counts

Question 7

Bimodal distribution

Answer 7

When distributions show 2 or more OBVIOUS peaks-> 2 different categorical wholes that are mostly polarized because of CIRCUMSTANCES attached to each
Eyeball-> if there is an obvious peak, but unlike unimodal peaks, the rest of the bins don’t cascade down in size, ONE is brave enough to stick out
EX: westerners are guaranteed less variability in our life expectancy

Question 8

“More than 100” (dot plot)

Answer 8

Dots on 100 do NOT count

Question 9

Center

Answer 9

most obviously the center numerical variable, not mean or typical value

Question 10

N=

Answer 10

When it says “n=“ this gives the total number of dots on the graph
ALSO is the total number of numbers for the mean

You can also deduce whether or not there are significantly less of a CW when looking at how much less they show up in comparison to the other CW in a study with two graphs (gender)

Question 11

Eyeballing variablity

Answer 11

measure variability by eyeballing it
1. Find center
- least variability= MOST dots/ values in center (EVERY girl has this!- nobody’s different smh)
- most variability= MOST sparsed dots/ values (balance= variability)

Question 12

Histograms rules

Answer 12

Have frequency indicator on side IN PLACE of the dots that we could easily count before (for gauging like we did with dots)
Running number line so bars have to touch each other.
Rules:
- first post of bin counts but not its second
- any data value that lands ON a post (1st or second) automatically belongs in the bin to its right (therefor is represented by this bin + classified by it)

Question 13

Relative frequency histograms

Answer 13

How much a percent is representative of a whole- frequency/ total
Y axis takes the frequency (count) of the numerical VALUES per numerical VARIABLE, then divide that by the total number of entries
Percentage of how much Numerical data falls into this bar (the one that matches it in height) using the total as reference
EX: bar at 5 counts -> 5/28 -> its now at 0.18 (18%) (SAME HEIGHT)
Find percentage of the relative frequencies accounted for within a certain amount of numerical values-> add the two relative frequencies you find
TIP- 4/100
We do this so we can see it through its accurate *LIKLIHOOD of showing up (counts aren’t enough)

Question 14

Histograms on stat crunch

Answer 14

Making bins too small-> too much data to look at
Distorts data because there is a lot of information between TOO wide bars

Question 15

Average on histogram

Answer 15

Locate bins according to what they ask for AND the bin rules
Measure the frequency of those bars (height)
Add up all the frequencies within your range
Then divide by total (will be given or just add up frequencies)

Question 16

Adding up bars/ range, not total

Answer 16

3 up to, but not including 6
First post ——> not last post

Question 17

Reading relative frequency

Answer 17

4/100

Question 18

Finding typical value/ comparing higher means

Answer 18

Eyeball it
Choose the bins that are more towards the other bins (rigth next to iT) that is SECOND largest bin on right or left side of it)
EX: don’t choose 0 or 1 if 1 is largest but 0 is significantly smaller
You scope out which bins can approximate an accurate center
Basically MEAN

Question 19

Reading frequencies (not relative)

Answer 19

Identify a bars frequency by “Between 80 and 100”
80- the value you eyeball it at
100- the tick mark value you actually measure it up to

When percentage is asked for this frequency (s) ->
“Between % and %”

Question 20

Predicting shapes of distributions

Answer 20

Right-skewed= outliers on right-> represent MORE than the NV (normal result is typically on the left side so it is low here)
* its about the context (7 days) -> it depends on if the greater you go up on the number line, the more you actually go up in your context
Left-skewed- most values are large (on right since larger values are farther up on number line) but there are outliers that take up a lot of space

Question 21

Comparing typical values (centers)

Answer 21

Look at the tallest bins (typical value card) BUT make sure to compare the values UNDERNEATH those bins

Question 22

Tip

Answer 22

Really make sure you’re looking at the right thing they want you to look at (higher monthly cost-> NV NOT relative frequency)

Question 23

The skinny bars

Answer 23

Are just dots

Question 24

Reading graph

Answer 24

The bottom tells all CONTEXT needed
Words- NV
Numbers- numerical values of that numerical variable
Y axis, unimortNt to actual NVs but how much they responded yes to NV

Question 25

UD SD

Answer 25

“With a SD of 2.24” = ONE SD equals 2.24 inches / distance between each tick mark is 2.24