What is a population:
A population consists of all the members of a group about which you want to draw a conclusion
What is a sample:
A sample is the portion of the population selected for analysis
What is a parameter:
A parameter is a numerical measure that describes a characteristic of a population
What is a statistic:
A statistic is a numerical measure that describes a characteristic of a sample.
N.B Statistics are subject to ‘sampling error’ and sampling can only provide an estimate average, so not always reliable.
What is the difference between a categorical and a numerical variable?
Categorical data can only be named or categorized (e.g. Political inclination, gender, satisfaction with a meal (very good, good, average…), Level of education (primary, secondary, tertiary)
Numerical data is measured on a natural numerical scale (e.g. Age, Results for BSB123, number of people with red hair in a lecture, share price)
What is a Descriptive statistic, and what is an Inferential statistic?
A descriptive statistic could be: Collect data (e.g. Survey), Present Data (e.g. Tables and Graphs), Characterise data (e.g. Sample mean)
What is the difference between a discrete and a continuous variable?
Discrete random variables produce numerical responses that arise from a counting process – e.g. full numbers (can you have half a person in a lecture? No. 1, 2, 3, 4 etc.)
Continuous random variables produce numerical responses that arise from a measuring process. (e.g. time travel to work 53.234 minutes. Could be 1.1, 1.12, 1.13 etc to infinity)
What is the difference between Ordinal and Nominal categorical data?
Nominal – no natural or implied order
E.g. mode of transport taken today – car, bus, train, horse, walk, cycle
No response is considered better, e.g. car is not better than horse
Ordinal – where there is an order to the categories.
E.g. rating a meal – very good, good, average, poor or very poor.
According to Road Patrol, the magazine of the RAC of Western Australia the LiveSafe survey reveals that nearly 80% of seniors feel that crime is increasing in WA, compared with 40% of students (Road Patrol, Royal Automobile Club of WA, October/November 2005). More than 1,300 students and seniors took part in the survey during RAC Community Education presentations. More than 25,000 students, parents and seniors across WA participate in these presentations each year.
(a) Describe the population for the RAC survey.
The population is all all students and seniors which took part in the RAC survey.
(b) Describe the sample for the RAC survey.
The sample is the 1,300 students and seniors that took part in the survey.
(c) Seventy-five per cent of students surveyed said they felt safe in their homes at night. Is this a parameter or a statistic?
Statistic – because only 1,300 students took part in the survey it is only a sample of the population and does not show the whole populations.
For each of the following variables, determine whether the variable is categorical or numerical. If the variable is numerical, determine whether the variable is discrete or continuous. If the variable is categorical, determine whether the variable is nominal or ordinal.
(a) Number of telephones per household
Nominal - discrete
(b) Length (in minutes) of the longest long-distance call made per month
Nominal – continuous
(c) Whether there is a telephone line connected to a computer modem in the household
(d) Categorical, nominal
(e) Whether there is a fax machine in the household