descriptive statistics

Question 1

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Tools for Continuous data<!--EndFragment-->

Answer 1

—Graphs
—Histograms
—Cumulative Relative Frequency plots (ogives)
—Stem and leaf plots
—Boxplots
—Line chart for data against time
—Middle – mean, median
—Spread – variance, range, quartiles

Question 2

types of data

Answer 2

—categorical or numerical

—Other sorts of information – e.g. comments in interview/survey – qualitative

Question 3

what does categorical data consist of

Answer 3

—nominal

ordinal

Question 4

what does numerical data consist of?

Answer 4

—discrete (count data) or continuous (also called interval)

Question 5

what is nominal data?

Answer 5

type of categorical data

faculty of study, eye colour, job, no order,

Question 6

what is ordinal data?

Answer 6

type of categorical data
—there is order: rank teaching as poor/fair/good/verygood

Question 7

tools for categorical data

Answer 7

—Graphs
—Bar charts (different to histograms – you can mix up order of columns and it still makes sense)
—Pie charts (use with caution)
—Numeric
—Mode – most frequently occurring observation
—Frequency of each category
—Examples in Minitab

Question 8

what are different types of modality a histogram can show?

Answer 8

—uni-modal, bi-modal, tri-modal, multi-modal

Question 9

bimodal histogram

Answer 9

Question 10

how to interpret histogram?

Answer 10

• *—Modality** – uni-modal, bi-modal, tri-modal, multi-modal
• *—Modal class** – class with highest number of observations (“modal class is centred at approximately…”)
• *—Skewness vs symmetry**—

Could choose instead a relative frequency histogram: replace frequency for each class by

class frequency/total number of obs.

Question 11

what is a disadvantage of using a histogram?

how may this be resolved?

Answer 11

—actual observation is lost by being grouped

—The stem and leaf display is an attempt to get similar information as a histogram, but without losing the actual observations

Question 12

steps to creating a stem and leaf plot

Answer 12

—Step 1: split each observation into a stem and a leaf, e.g.
—If observations are (1.2, 1.5, 2.9 ….); stem = unit; leaf = decimal
—If observations are (42.1, 38.4, 53.8….); stem = tens, leaf = units (or unit-decimal)

—Step 2: write stems in left column; put leaves in right column.

Question 13

features of stem and leaf plot

Answer 13

Question 14

what is Cumulative Relative Frequency Distribution

Answer 14

—Relative frequency distribution histogram – proportion in each class
—Cumulative relative frequency distribution – proportion up to and including that class
—Ogive – graph of cumulative relative frequencies; also called empirical cumulative density function

Question 15

what does cumulative density function look like?

Answer 15

Question 16

how to calculate length of whisker?

Answer 16

1.5 x interquartile range

Question 17

how to calculate location of percentiles in boxplot?

Answer 17

Question 18

Answer 18

Question 19

Which measure of centre is best?

for continuous data

Answer 19

Mean generally most commonly used; but it is sensitive to extreme values
—If data skewed/extreme values present, median better, e.g. real estate prices (we say the median is robust to outliers)
—Mode generally best for categorical data – e.g. restaurant service quality (below): mode is very good. (ordinal)

Question 20

differences between population and sampel

Answer 20

—Populations have parameters – certain true values which describe them. E.g. if we measure every individual, we can calculate the exact average and exact variance of the population. These are called population parameters.

a sample we calculate statistics, or estimates of the parameters. Use sample statistics to approximate population parameters. E.g. from a sample we can estimate the true population mean by using the same mean; if we have a sample standard deviation, we can estimate the population standard deviation.

Question 21

calculate covariance and correlation

Answer 21

Question 22

correlation formula for population and for sample

Answer 22