V4

Question 1

definition statistics

Answer 1

statistics is the study of the collection, analysis, interpretation, presentation, and organisation of data

Question 2

univariate analysis

Answer 2

single variable

Question 3

bivariate analysis

Answer 3

multiple variables

Question 4

name the different means

Answer 4

• arithmetic mean (used the most)
• geometric mean (# are more dispersed)
• harmonic mean

Question 5

geometric mean

Answer 5

• a geometric mean is often used when comparing different items that have different numeric ranges
• finding a single “figure of merit for these items”
• so measurements can be “equal”

Question 6

harmonic mean

Answer 6

situations involving rates and rations, it then provides he truest average

• for example 60 km/h
• > the variable needs to be part of the ratio (for example km)

Question 7

important arithmetic mean parameters

Answer 7

trim() - fraction of observations to be trimmed from each end of x before the mean is computed -> remove extreme outliers
na.rm() - indicating whether NA values should be stripped before computation proceeds

Question 8

Median

Answer 8

• the number separating the higher half of data from the lower half (advised to always use this)
• can be found by arranging all valued from lowest to highest value and picking the middle one
• in case of an even number of values, the median is then usually defined to be the arithmetic mean of the two middle values
• code : median()

Question 9

important parameters mean

Answer 9

na.rm() - indicating whether NA values should be stripped before computation proceeds

Question 10

mode

Answer 10

• value that appears most often in a set of data
• numerical value of mode is same as that of the mean and median in a perfect normal distribution (Gaussian distribution)
• but will be very different in highly skewed distributions

Question 11

dispersion

Answer 11

• range of a data set is known as the difference between the min and max
• range() - gives min and max valued
• diff(range(x)) gives is the range of the input

Question 12

Quantiles

Answer 12

• dividing ordered data into q essentially equal-sized data subsets is the motivation for q-quantiles
• median = half quantile
• quantiles are the data values marking the boundaries between consecutive subsets
• 9 different types of quantile computation
• quantile()

Question 13

Variance

Answer 13

• variance measures the spread of a set of numbers
• variance of zero indicated that all the values are identical
• variance is always non-negative
• var()

Question 14

standard deviation

Answer 14

• a measure that is used to quantify the amount of the variation or dispersion of a set of data values
• a standard deviation of 0 indicates data points tend to be very close to the mean
• sqrt(var(x)) or sd(x)

Question 15

Outliers

Answer 15

• an observation point that is distant from other observations
• depends on variability in the measurement
• heavy-tailed distribution - kurtosis
• experimental error
• is an observation an outlier ? Subjective - Winsorising -> adjusting data point or change data to mean

Question 16

skeweness

Answer 16

• measure of the asymmetry of a distribution
• long tail , fat tail
• in R: library(psych) -> skew(x)

Question 17

Kurtosis

Answer 17

• measure of the “peakedness” of the distribution
• Mesokurtic - zero excess kurtosis
• leptokurtic - positive excess kurtosis (higher)
• platykurtic - negative excess kurtosis (lower)
• in R: library(psych) -> kurtosi()

Question 18

when is distribution important ?

Answer 18

• many models assume a normal distribution of the input distribution or the error term
• shapiro-Wilk test of normality (5% error margin) - shapiro.test(x) p>0.05 normal distribution
• > always good to plot/check distribution with other factors

Question 19

plot()

Answer 19

• create a plot window and call points() on x

Question 20

points()

Answer 20

• create a dot/line plot of the data in x

Question 21

axis()

Answer 21

axis(side, at(where), labels(what))

Question 22

image()

Answer 22

• useful when you have a matrix

- create a heat map (2D plot) of the data

Question 23

boxplot()

Answer 23

• produce box-and-whisker plots
• notch - if the notches of two plots do not overlap this is ‘strong evidence’ that the two means differ
• varwidth - boxes are drawn with widths proportional to the sqrt of # of observations of group

Question 24

histogram

Answer 24

• hist()
• freq - representation of frequencies
• breaks - breakpoints between histogram cells
• plot - should a histogram be plotted

Question 25

heatmap()

Answer 25

• plot a matrix, rows that are similar are put together

- image plot combined with automated clustering and side colours (groups)

Question 26

par()

Answer 26

used to set or query graphical parameters
options - put .lab or .axis to specify what to apply on
- cex -> magnification
- family, font
- lab, las, lay -> line/label type
- mai, mar, mex -> different typed of margins
- marrow, mccollum -> multiple plots in matrix shapes
- pch -> size of point, will multiply everything for Pdf
- x-axis, xaxt -> control xaxis

Question 27

steps in plotting (coding)

Answer 27

# create an output device
png("my.png", width = 100, height = 100)
#setup parameters
par() -> set up everything you need
# create an empty plot
plot(x = c(0,100), y = c(0,100), type = 'n') 'n' makes empty plot
# add points/lines/arrows
points(mdata)
#save the plot the png
dev.off()

Question 28

make multiple plots simple (code)

Answer 28

par(mfrow = c(2,2)) # 4 plots in 2 rows 2 col
# create 4 seperate plots after

Question 29

more complex multiple plots

Answer 29

• layout()
• layout.show() to get a preview

nf

Question 30

apply and subset example means

Answer 30

apply(subset(mdata, select = c(“col1”, “col2”)), 2, mean)

Question 31

get means for a certain number of columns and use a column filter

Answer 31

apply(subset(mdata, Temp < 25, select = c(“col1”, “col2”)), 2, mean)