statistics

Question 1

kinds of variables

Answer 1

1. categorical (qualitative)
2. numerical (quantitative) => discrete (counting), continuous (measuring)

Question 2

population def and kinds

Answer 2

= set from which the data is collected
finite (everything in life), inifinite (math concepts)

Question 3

sampling

Answer 3

= selecting the group from which data is collected from

Question 4

sampling methods

Answer 4

1. statistical (selection based on chance)
2. non-statistical (selection based on convenience)

Question 5

statistical sampling methods

Answer 5

1. simple random sampling => every possible sample of a specific size has an equal chance of being chosen
2. stratified => a population is divided into strata based on the values of interest and then random sampling within strata
3. systematic => first element is selected randomly and then each nth element (sampling interval) is selected

Question 6

non-statistical sampling methods

Answer 6

1. quota sampling => non-random selection of a predertermined number of units
2. availability sampling => based on convenience

Question 7

statistical interferences

Answer 7

= using characteristics of a sample to draw conclusions

Question 8

descriptive statistics

Answer 8

displaying and summarizing data

Question 9

infernal statistics

Answer 9

choosing a representative sample, drawing conclusions from sample to population, predict, …

Question 10

absolute vs relative frequency

Answer 10

absolute = number of data
relative = abs/number of total data

Question 11

cumulative absolute vs relative frequency

Answer 11

cum. abs. => less or equal absolute frequency (final = total number of data)
cum. relative => less or equal relative frequency (final = 100%)

adding consecutive

Question 12

width, class width

Answer 12

width => difference between subsequent grades
class width = beginning of next class - beginning of said class

Question 13

class boundaries

Answer 13

• upper class of previous = lower class of current
• class width is evident

Question 14

histogram

Answer 14

• = graphical representation of a frequency distribution table
• used for numerical values
• no spaces between columns
• variable axis has direction

Question 15

bar graph

Answer 15

represents qualitative data
variable axis has no direction

Question 16

distribution curve

or ogive

Answer 16

= smooth histogram, indicating the general behaviour of the histogram

Question 17

distribution in a distribution curve

Answer 17

• symmetrical
• skewed to the left
• skewed to the right

Question 18

modality of a distribution curve

Answer 18

1. unimodal => one peak
2. bimodal => two peaks
3. trimodal => three peaks

height of peaks doesn’t matter

Question 19

uniform distribution

Answer 19

• straight line histogram
• each class has roughly the same distribution

Question 20

bell-shaped distribution

Answer 20

unimodal, symmetric distribution
Gaussian (normal) curve

Question 21

approximation of central tendencies on a distribution curve

Answer 21

• mode => x-coordinate of the highest peak
• median => x-coordinate of the vertical line that halves the area of the distribution curve
• mean => symmetric distribution (coincides with the median and mode at the center of distribution), skewed (to the side of the tail of the median)

Question 22

measures of central distribution

Answer 22

• mode = value with the highest frequency
• median = value in the middle position of data in ascending order
• arithmetic mean (average) = sum of all data/number of data

Question 23

modal class

Answer 23

class with the most elements

Question 24

average of data in k classes with mid-interval values m1, m2, …, mk

Answer 24

(m1f1 + m2f2 + … + mkfk)/n

Question 25

measures of spread (variability)

Answer 25

how well the typical value represents the list range, variance, standard deviation, interquartile percentiles

Question 26

range

Answer 26

largest value - smallest value

Question 27

variance

Answer 27

V = sum of the differences squared of a value from the mean = sum of squared values - squared average

Question 28

sample variance

Answer 28

s^2 = (sum of the differences of values to the average squared)/(n-1)

Question 29

percentiles

Answer 29

seperate large ordered data sets into humdredths C1, C2, ..., C99

Question 30

quartiles | +interquartile range

Answer 30

seperate data into 4 quarters Q1, Q2 (median), Q3 IQR = Q3 - Q1

Question 31

five-number data summary

Answer 31

* x min, Q1, Q2, Q3, x max * exludes outliers * box and whiskers plot graphically depicts the summary

Question 32

exclusion of outliers

Answer 32

* all data outside of [lower fence, upper fence] are outliers * lower fence = Q1 - 1.5IQR * upper fence = Q3 + 1.5IQR

Question 33

bivariate analysis

Answer 33

* analysis of **2 variables**, generally **their corrolation**, over the same population * the **explanatory** (independant) variable seemingly explains the change in the **response** (dependant) variable * graphically represented with a **scatter plot**

Question 34

linear corrolation

Answer 34

* how close to a line points in a scatter plot are * represented with Pearson's (product-moment) correlation coefficient

Question 35

weak, moderate, strong, perfect, no correlation

Answer 35

* weak => weakly represents a line * moderate => slightly resembles a line * strong => close to a line * perfect correlation => forms a line * no correlation => no line

Question 36

Pearson's (product-moment) correlation coefficient | range, undefined, sample vs population

Answer 36

* -1 ≤ r ≤ 1 * does not measure gradient * horizontal line => r is undefined * sample r = population r

Question 37

value of r means

Answer 37

* r > 0 => increasing line * r < 0 => decreasing line * r = 1 => perfect positive correlation * r = -1 => perfect negative correlation * r = 0 => no correlation

Question 38

regression line (model)

Answer 38

= line of best fit, trend line = a line that represents points in a plane as good as possible => the line that minimizes the sum of squares of vertical distances to the line minimal d1^2 + d2^2 + ... + dn^2 is the best

Question 39

regression line of y on x | form of line, what it does, GDC, used for

Answer 39

* **y = ax + b** * minimizing the **vertical distances** to the line * GDC: **X on Xlist**, Y on Ylist (*y = ax+b*) * used to **estimate values of y** given x

Question 40

regression line of x on y | form of line, what it does, GDC, used for

Answer 40

* **x = ay + b** * minimizing the **horizontal distance** to the line * GDC: **Y on Xlist**, X on Ylist (*y=ax+b*) * **estimation of values of x** given y

Question 41

where do regression lines y on x and x on y meet

Answer 41

at (average of x, average of y)

Question 42

interpolation

Answer 42

estimation of y given x inside the data, usually more accurate

Question 43

extrapolation

Answer 43

* estimation of y given x outside the given data * we don't know the relationship of variables outside the given data set => less accurate * aim to extrapolate close to the given data