CHAPTER 1- UNIVARIATE DATA Ex 1A- Types of Data Ex 1B- Stem Plots Ex 1C- Dot Plots, Frequency Histograms and Bar Charts CORE-DATA ANAYLSIS Miss. Tran

EX 1A- TYPES OF DATA Univariate Data- data with one variable. Eg: number of cars sold per week Biavariate Data- sets of data that contain two variables. Eg: height and nationality, height and weight, gender and religion Multivariate Data- data with more than two variables.

Numerical DataCategorical Data Discrete (countable in whole numbers) Continuous (measureable with fractions and decimals) Eg: Number of people living at your home Eg: Height, Weight, Time Categories Eg: genders, AFL football teams, religions, finishing positions in Melbourne Cup, ratings of 1-5 to indicate preferences for 5 different cars, age groups (0-9, 10-19, ), hair colours Note: Some numbers may look like numerical data, but are actually names or titles eg: ratings of 1 to 5 given to different samples of cake- ‘This one’s a 4’. They are not countable and are place the subject in a category.

TEST YOUR UNDERSTANDING 1 Write whether each of the following represents numerical or categorical data. For eache set of numerical data identified, state whether the data are discrete or continuous. a The heights, in centimetres, of a group of children b The diameters, in millimetres, of a collection of ball-bearings c The numbers of visitors at a display each day d The modes of transport that students in Year 12 take to school e The 10 most-watched television programs in a week f The occupations of a group of 30-year-olds g The numbers of subjects offered to VCE students at various schools h Life expectancies i Species of fish j Blood groups k Years of birth l Countries of birth m Tax brackets

2. An example of a numerical variable is: A attitude to 4-yearly elections (for or against) B year level of students C the total attendance at Carlton football matches D position in a queue at the pie stall E television channel numbers shown on a dial 3 The weight of each truck-load of woodchips delivered to the wharf during a one-month period was recorded. This is an example of: A categorical and discrete data B discrete data C continuous and numerical data D continuous and categorical data E numerical and discrete data

EX 1B- STEM PLOTS A way of displaying a set of data (Order is important). Best suited to data which contain up to about 50 observations/records. It is constructed by splitting the numerals of a record into two parts-the stem and leaf’ Stem- the preceding digits before the last digit Leaf- the last digits Eg: The stem plot below right shows the ages of people attending an advanced computer class. The ages of the members of the class are 16, 22, 22, 23, 30, 32, 34, 36, 42, 43, 46, 47, 53, 57 and 61.

STEM PLOTS WITH DECIMALS The masses (in kilograms) of the members of an Under-17 football squad are given below Display the data in a stem plot. Lowest number = 65.1 Highest number = 75.6 Use stems from 65-75

STEM PLOTS THAT ARE BUNCHED To get a clear idea about the data variation, we can split the stems into halves or fifths. Halves- 1 st half has any leaf digits in the range nd half has any leaf digits in the range 5-9 (appears next to the stem with *) Fifths- each stem appears 5 times - 0s and 1s -2s and 3s -4s and 5s -6s and 7s -8s and 9s

A set of golf scores for a group of professional golfers trialling a new 18-hole golf course is shown on the following stem plot. Produce another stem plot for these data by splitting the stems into: a) halves

A set of golf scores for a group of professional golfers trialling a new 18-hole golf course is shown on the following stem plot. Produce another stem plot for these data by splitting the stems into: b) fifths

Ex 1C- Dot plots, frequency histograms and bar charts This is another form of displaying data in graphical way. DOT PLOTS Dot plots are used to display discrete data where values are not spread out very much. They are also used to display categorical data.

TESTING YOUR KNOWLEDGE The number of hours per week spent on art by 18 students is given below Display the data as a dot plot. Lowest score = 0 Highest score= 5

Frequency Histograms It is a useful way of displaying large data sets of over 50 observations/records. The vertical axis = frequency The horizontal axis= class intervals eg: height, income etc When data are in raw form (a list of figures in no particular order)- it is helpful to first construct a frequency table.

Frequency Histograms Construct a frequency table and histogram for the following set of data, which indicates the number of hours of homework undertaken by 16 students in a day FrequencyHours FrequencyHours

CASIO CLASS PAD

HISTOGRAMS WITH CONTINUOUS DATA The data below show the distribution of masses (in kilograms) of 60 students in Year 7 at Strathmore Secondary College. Construct a frequency histogram to display the data more clearly Class intervalTallyFrequency 30–34.9I1 35–39.9IIII4 40– – – – –64.9III3 Total60 Minimum value = 34.2 kg Maximum value = 62.3 kg Say we start from 30kg to 65kg, we would then have a range of 35. If each interval was 5kg, we would then have 7 intervals which is reasonable. Note: Somewhere between about 5 and 15 class intervals are usual.

Then the histogram would look like: Class intervalTallyFrequency 30–34.9I1 35–39.9IIII4 40– – – – –64.9III3 Total60

TESTING YOUR KNOWLEDGE The marks out of 20 received by 30 students for a book-review assignment are given in the frequency table below. Mark Frequency Display these data on a histogram.

Bar Charts It is similar to a histogram. It consists of bars of equal width separated by small, equal spaces and may be arranged either horizontally or vertically. Often used to display categorical data. The frequency is graphed against a variable.

Segmented Bar Charts It is a single bar which is used to represent all the data being studied. It is divided into segments, representing a particular group of data. Generally presented as percentages and so the total bar length is 100% of the data.

Segmented Bar Charts Road traffic accidents involving fatalities Accidents involving fatalities YearNSWVic.OldSAWATas.NTACTAust

YearNSWVic.OldSAWATas.NTACTAust StateNumber of accidentsPercentage NSW ÷ 1584 × 100% = 30.7% Vic ÷ 1584 × 100% = 25.5% Qld ÷ 1584 × 100% = 18.7% SA ÷ 1584 × 100% = 8.6% WA ÷ 1584 × 100% = 9.5% Tas.5252 ÷ 1584 × 100% = 3.3% NT4343 ÷ 1584 × 100% = 2.7% ACT1515 ÷ 1584 × 100% = 0.9%

Exercise 1D- Describing the shape of stem plots and histograms When data are displayed in a histogram or a stem plot, we look into its distribution. Symmetric Distributions Skewed Distributions

SYMMETRIC DISTRIBUTIONS The spread of the data Symmetric distribution (single peak and the data trial off on both sides of this peak in roughly the same fashion)

Is this a positively or negatively skewed distribution?? Positively Skewed

What type of distribution is this?? Symmetric Distribution

CLASSWORK/HOMEWORK Complete Ex 1B pg 6 Q’s 2, 4, 6-10 Complete Ex 1C pg 12 Q’s 4, 5, 6 Complete Ex 1D pg 15 Q’s 1-9