Task 2 the characteristic score

Question 1

Cases

Answer 1

are the objects described by a set of data (customers, companies, subjects ín a study)

Question 2

Label

Answer 2

is a special variable used in some data sets to distinguish the different cases

Question 3

Variable

Answer 3

is a characteristic of a case

→different cases can have different values of the variables

Question 4

Categorical Variable

Answer 4

A categorical doesn’t have a numerically meaning, it describes simply the quality or characteristics of a variable. The numbers in categorical variable designate quality rather than a measurement quality. You could use e.g. gender and use a 1 for males and a 2 for females. You can’t calculate with these numbers

Question 5

Quantitative Variable

Answer 5

Quantitative variables are measured and expressed numerically, have numeric meaning and are used for calculation. Although e.g. zip codes are written in numbers these numbers are only labels and you can´t calculate with them

Question 6

Nominal Variable

Answer 6

Nominal variables are categorical. They are equal categories in other words categories which don’t differ in terms of order. You can’t bring them order you cant calculate with them e.g. Gender (Male, Female, Transgender) Eye colour (Blue, Green, Brown, Hazel)

Question 7

Ordinal variable

Answer 7

Ordinal variables, belong to categorical variables, are those which have a clear ordering e.g. education status middle school, high school, college now you have 1 2 and 3 and they have a clear order. Economic status: low middle high again 1 2 and 3 in a clear order

Question 8

Interval Variable

Answer 8

Interval belongs to quantitative variables and it means that the interval between the values has the same interval/ are equally spaced (same space in between). In other words the distance between the variables must be the same E.g. Three peoples income 15,000 20,000 and 25,000 the interval is always 5,000

Question 9

Distribution of variables

Answer 9

It tells us what values a variable takes and how often it takes these values

Question 10

Frequency table

Answer 10

You can see the peak or Two peaks (bimodal). Used for categorical variables (nominal/ordinal)

Question 11

Pie chart

Answer 11

We can se the proportions and what is the major variable and what the minor
Nominal variables

Question 12

Bar chart

Answer 12

Lower form of frequency and mostly used with categorical variables preferred in case of ordinal ones but also applicable with nominal variables

Question 13

Stem-and-leaf plot

Answer 13

We can see the peak and the outliers it is basically just a frequency table turned around
For both quantitative variables so interval and ratio

Question 14

Distribution: Shapes

Answer 14

Trends, Peak, Outlier

Question 15

skewed distribution

Answer 15

A frequency distribution in which most scores fall in categories above or below the middle

Question 16

Histogram

Answer 16

useful for quantitative variables

Question 17

Mode (MO)

Answer 17

Simply the score that occurs most often

Tells something about the frequency of score

Question 18

Median (M)

Answer 18

Lies in the middle if we order the sores from highest to lowest
Take the total amount of sores (N) +1 and divide it by 2 to obtain the middle score rank((N)+1)/2= middle score rank
You count to the Median and take the value of this score

Question 19

Arithmetic mean ( x ̅)

Answer 19

Add up all the separate scores and divide them by the total of scores (N)
x ̅=(∑x_i)/N

Question 20

Sum of squares (variation)

Answer 20

Calculate the difference of each score from the mean and square all the differences before adding them up
∑(x_i-x ̅ )^2

Question 21

Variance

Answer 21

divide the variation by the total amount of scores (N) minus 1
s_x^2=(∑(x_i-x ̅ )^2)/(N-1)=variance

Question 22

Standard deviation

Answer 22

Take the square root of the variance

s_x=√((∑(χ_i-x ̅ )^2)/(N-1))

Question 23

Split up in quartiles (Q1, Q2, Q3)

Answer 23

first quartile(Q1): 25% of all score lie below it and 75% above 
second quartile(Q2): The median
third quartile(Q3): 75% lies below 25% above

Question 24

IQR (interquartile range)

Answer 24

between Q1 and Q3 lies the half of the scores

IQR= Q3-Q1

Question 25

Five Number Summary

Answer 25

the lowest score (minimum), Q1, the median, Q3, and the highest score the maximum. You can leave out the outliers.
→can be summarised in a boxplot (all the horizontal bars indicate a number from the summary

Question 26

1,5*IQR criterion

Answer 26

Used to identify outliers: Q1-(1,5IQR)= every score below the outcome is an outlier
Q3+(1,5IQR)= everything above is an outlier

Question 27

Linear Transformation

Centering

Answer 27

Shift all the scores such that the scale becomes 0
→subtract the mean from all scores →C=X - x ̅

Shape of distribution is not effected at all

Question 28

Z-scores

Answer 28

Z-scores indicate how many standard deviations a measurement has scored above or below the mean
z=(xi-x ̅)/s_x

Question 29

Centring

Answer 29

Shift all the scores such that the scale becomes 0
→subtract the mean from all scores →C=X - x ̅
Shape of distribution is not effected at all
Standard deviation does not change

Question 30

Standardising

Answer 30

Make sure that the scale obtains a mean of 0, and a standard deviation of 1
The results are so-called z-scores
→z=(xi-x ̅)/s_x
Z-scores indicate how many standard deviations a measurement has scored above or below the mean

Question 31

Multiplying

Answer 31

• We multiply all the scores by a certain number

→e.g. for every sold litre you get 20$ so you multiply your X with 20

Question 32

order of mean median mode in view of skewing

Answer 32

right skewed Mean > Median > Mode

left skewed Mean < Median < Mode