Basic Descriptive Statistics

Question 1

what are statistics?

Answer 1

branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data

Question 2

what are descriptive stats?

Answer 2

summarizes or describes the characteristics of a data set

Question 3

what are examples of descriptive stats?

Answer 3

measures of central tendency (mean, median, mode), measures of variability (spread), and frequency distribution (count)

Question 4

inferential stats?

Answer 4

involves the use of a sample to estimate some characteristics in a large population and/or test a research hypothesis about a given population

Question 5

primary data

Answer 5

acquired directly from source

Question 6

secondary data (or archival data)

Answer 6

collected by someone else

Question 7

nominal data and example

Answer 7

categories without any inherent order or meaningful sequence

ex: fruit colors

Question 8

ordinal data and example

Answer 8

ranked data

ex: strongly agree to strongly disagree

Question 9

interval data and example

Answer 9

data with ordered categories and equal intervals between them with no true zero point

ex: temperature

Question 10

ratio data and example

Answer 10

data with ordered categories and equal intervals between them with a true zero

ex: height, weight, age, income

Question 11

measures of central tendency definition

Answer 11

univariate statistic that indicates the average observed value of a variable in a data set or the center of the frequency distribution of the data set

Question 12

what is the median?

Answer 12

variable in the middle, splitting is 50/50

Question 13

if the distribution is symmetric, mean and median are same/different?

Answer 13

Same

Question 14

if distribution almost symmetric, mean and median are ___

Answer 14

almost the same

Question 15

if the distribution is skewed, the mean is pulled in the direction of…

Answer 15

the long tail

Question 16

what does it mean to have have unstable median?

Answer 16

the median value of a dataset or distribution fluctuates or is sensitive to small changes in the data

Question 17

is the median resistant to ouliers?

Answer 17

yes

Question 18

what is mode

Answer 18

most frequent value (value not the frequency itself)

Question 19

what type of data is mode most commonly used for?

Answer 19

nominal because it identifies the most frequent category

Question 20

measures of dispersion

Answer 20

descriptive stats that describe how similar a set of scores are to each other

Question 21

the most similar the scores are to each other, the ____ the measure of dispersion will be

Answer 21

lower

Question 22

the less similar the scores are to each other, the ___ the measure of dispersion will be

Answer 22

higher

Question 23

a taller curve has ___ dispersion, a flatter curve has ___ dispersion

Answer 23

less, more

Question 24

when would you use range?

Answer 24

when you have ordinal data or you are presenting your results with little or no knowledge of stats

rarely used as it is fairly insensitive

Question 25

what is the interquartile range (IQR)?

Answer 25

the range of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1)

Question 26

what is the semi-interquartile range (SIR)?

Answer 26

half the interquartile range (difference between Q1 and Q3 divided by 2)

Question 27

what is variance?

Answer 27

it tells you how far, on average, each data point is from the mean (average) of the dataset

Question 28

how do you solve for variance?

Answer 28

subtract the mean from each score and square, then divide by number of data

Question 29

the larger the variance, the ___ the scores deviate away from the mean

Answer 29

more

Question 30

why is the formula for variance of a sample different from formula for population variance?

Answer 30

because the sample mean is not a perfect estimate of the population mean

Question 31

degree of freedom

Answer 31

the number of values that are free to vary when calculating a statistic Degrees of freedom help account for the fact that some of the data is already used up in estimating certain values (like the mean), so fewer data points are "free" for calculating other statistics

Question 32

what is standard deviation

Answer 32

the square root of the variance a measure of how much the values in a dataset tend to differ from the average (mean) value

Question 33

why do we use SD instead of variance?

Answer 33

because squared numbers are awkward to use

Question 34

what is coefficient of variation

Answer 34

shows how much variability or spread there is in a dataset relative to the mean (average) of the data. It’s often used to compare the variability between different datasets, especially when they have different units or scales.

Question 35

formula for CV

Answer 35

CV = S/X bar(100)

Question 36

if data are symmetric, with no serious outliers, what measures of variabilities should be used

Answer 36

range and SD

Question 37

if data is skewed and/or have serious outliers, what measure of variability should be used

Answer 37

IQR

Question 38

if comparing variation across two data sets, what measure of variability should be used?

Answer 38

CV

Question 39

what is the notch?

Answer 39

helps you visually assess whether the medians of different groups are likely different or similar, based on confidence intervals.

Question 40

if two boxes' notches do overlap, there is ____ evidence their medians differ

Answer 40

strong

Question 41

what are error bars?

Answer 41

help indicate estimated error or uncertainty to give a general sense of how precise a measurement is

Question 42

histogram

Answer 42

bar graph of frequencies or percentages

Question 43

in a negatively skewed distribution, mean __ median

Answer 43

<

Question 44

in a positively skewed distribution, mean __ median

Answer 44

>

Question 45

what is sturges' formula?

Answer 45

used to determine the number of bins or intervals (also called "classes") to use when creating a histogram for a dataset.

Question 46

what is the mean center (centroid)?

Answer 46

central tendency of a group of points located on a Cartesian coordinate system average position of the points

Question 47

how to find mean center

Answer 47

get mean of x values and then on y values, those coordinates are mean center

Question 48

weighted mean center

Answer 48

some data is more important than others

Question 49

what is the median center (Euclidean median)

Answer 49

the point that minimizes aggregate distance to the center

Question 50

what is standard distance

Answer 50

measures how far data points are from a central value or from each other.

Question 51

standard deviational ellipse

Answer 51

graphical tool used to represent the variability and directionality of a set of data points in a two-dimensional space

Question 52

kernel density estimation

Answer 52

a method used to estimate and visualize the distribution of data points, creating a smooth curve that represents the underlying distribution

Question 53

what proportions and what are they useful for and give example

Answer 53

sum of proportions = 1 useful for comparing two sets of data with different sizes and category counts e.g. a different box of marbles gives a yellow proportion of 2/23, and in order for this to be a reasonable comparison we need to know the totals for both samples

Question 54

what is location quotient?

Answer 54

used to compare the relative concentration of characteristics in a specific area against a broader reference area

Question 55

standard error

Answer 55

a measure of the variability or dispersion of a sample statistic, such as the sample mean, from the true population parameter