Lecture 2 - Describing & Summarising Data + Normal Distribution

Question 1

measures of central tendency:

Answer 1

mode (most frequent value), arithmetic mean (n) & the median (middle value in ranked dataset)

Question 2

what measure of central tendency is affected the most by extreme values?

Answer 2

the mean is affected most by extreme values, the median would not be affected as much

Question 3

how do you round with your mean values?

Answer 3

you always round your mean values to one decimal place (e.g. 4.988 —> 5.000)

Question 4

what do histograms primarily show?

Answer 4

frequency

Question 5

what does a positive skew graph look like?

Answer 5

left-slanted bell shape

Question 6

what does a negative skew graph look like?

Answer 6

right-slanted bell shape

Question 7

the more variables in our data…

Answer 7

… the less certain we can be about the estimates from the data, such as the mean

Question 8

sum of squares:

Answer 8

total sum of squares = sum of all observations ( value in a sample - mean value of a sample)^2

Question 9

what is the problem with the sum of squares equation?

Answer 9

the more data points you have, the bigger the sum of squares value will be

Question 10

unreliability is proportional to:

Answer 10

variance

Question 11

standard deviation equation:

Answer 11

standard deviation = √sum of (each value - mean)^2 / size of population

Question 12

what does standard error of the mean calculate and how does it differ from standard deviation?

Answer 12

standard error calculates the scatter of the mean values, whereas the standard deviation is the scatter of the raw data values (observations)

Question 13

Two Standard Error rules of thumb:

Answer 13

1) standard error is a measure of how confident we are that our sample mean is close to the population mean

2) in 95.5% of cases the population mean will fall within ca. 2 standard errors of the sample mean

Question 14

Gaussian Distribution:

Answer 14

same as normal distribution it is a common continuous probability distribution

it is bell shaped asymptotic at the extremes and symmetrical around the mean with no skew: mean = median - mode

area under the curve is directly proportional to the relative frequency of observations and their probability (p)

Question 15

what is the Gaussian (Normal) Distribution important for?

Answer 15

statistical analysis

Question 16

describe the features of a box-&-whisker plot:

Answer 16

central line is median, the top line in the box is the 1st quartile, bottom line in the box is the 3rd quartile and the whole box itself is the interquartile range with the whiskers being the largest and smallest data values

Question 17

IQR equation:

Answer 17

IQR = [3rd Quartile] - [1st Quartile]

Question 18

what does the location of the median within a box plot give information regarding?

Answer 18

the placement of a median within the box plot gives information regarding skewness in a dataset

Question 19

what are the variabilities and uncertainties for the following central tendencies?

1) mean

2) median

Answer 19

mean = variance, SD, SE of the mean. 95% confidence interval

median = interquartile range

Question 20

standard error of the mean calculation:

Answer 20

standard error = SD / √No. of samples

Question 21

continuous variable:

Answer 21

values within a range, can be measured (e.g. size: 130cm, 27cm etc)

Question 22

discrete variable:

Answer 22

fixed values, integer, can be counted (e.g. no. of chromosomes)

Question 23

ordinal variable:

Answer 23

n factor levels with implicit order (e.g. size class: small, medium & large)

Question 24

nominal variable:

Answer 24

n factor levels without implicit order (e.g. eye colour: grey, blue, brown etc / treatment: sham vs. testosterone)

Question 25

two types of numerical (quantitative) variable:

Answer 25

continuous (within a range, measured) and discrete (in a range, counted)

Question 26

two types of categorical (qualitative) variable:

Answer 26

nominal (n factor levels without implicit order: eye colour, testosterone vs sham) and ordinal (n factor levels with implicit order: small, medium, large)