It all ADDS UP

Yeats College teacher Louise Geoghegan advises on how best to approach and prepare for Maths Paper 2

Statistics Students need to understand clearly the concepts behind collecting data, processing it and of course analysing the data.

TYPES OF DATA

This section of the statistics course involves learning and understanding the different types of data there are and learning about the different methods of collecting data.

Numerical data is data split into discrete and continuous:

Discrete data is data that has a specific number such as the number of students in the Maths class is 15.

Continuous data is data with a range of numbers such as the weights of students in the classroom may range from 50kg – 68kg.

Categorical data is data that fits into a group or a category such as the students in the class being either male or female.

Collecting data can occur in two ways:

Primary data collection is done by the person collecting the data or by someone on their behalf. This can be done by doing a survey, observation, experiments or doing a questionnaire.

Secondary data is collected by somebody else and it can be used by anyone. This can be done by using the Internet, contacting the Central Statistics Office and any articles/ publications that are available to the public. It is important that students understand the positives and negatives of each type of data.

When collecting data we choose a sample of the population being surveyed as using the entire population would cost too much money. Once we have the sample surveyed we can induce information about the entire population.

The size of the sample is important. If the sample is too small, the results may not be very reliable. If the sample is too large, the data may take too long to collect.

The sample you select for your study is very important. If the sample is not properly selected the results may be biased. If bias exists, the results will be inaccurate and so will not represent the whole population correctly. Bias in a sample may arise from any of the following:

• Not choosing the sample that represents the population

Example: Mary is doing a survey on the number of school students who buy their lunch in the school canteen. Taking a sample of students from the canteen in the school would be biased.

• Not identifying the correct population Example: John is doing a survey on the attitudes of young people towards fashion. Taking a sample of male students only would be biased.

• Failure to respond to a survey

Example: Many people do not fill in responses to questionnaires sent through the post. Those who do respond may not represent the population.

• Dishonest answers

If a proportion of the sample gives incorrect answers this will of course affect the conclusions about the entire population.

MEASURES OF LOCATION AND SPREAD Mean

This is another name for the average. Find the sum of the numbers and divide this sum by the number of numbers. The μ. symbol for mean is μ.

Mode

The number that is repeated the most.

Median

When numbers are placed in ascending/descending order the median is the middle number. If there is an even number of values in the set you get the average of the middle two numbers.

Range

The highest value in a set of data minus the lowest value. This shows the spread of the data. This is a basic measure of spread as it only takes into consideration the largest and smallest values.

Lower quartile

When data is arranged in descending/ascending order this is the value one quarter of the way into the data.

Upper quartile

When data is arranged in descending/ascending order this is the value three quarters of the way into the data.

Interquartile range

The upper quartile minus the lower quartile.

DISPLAYING DATA Bar charts

This consists of a series of bars of the same width, drawn either vertically or horizontally from an axis. The heights/lengths of the bars always represent the frequencies. The bars are generally separated by narrow gaps of equal length. The above bar chart shows the number of cars sold in Galway.

Line plots

A line plot is used to display small sets of discrete or categorical data. It is similar to a bar chart with dots or crosses used instead of a bar. Each dot represents one unit of the variable.