Graphical Techniques

Learning Objectives: 1) To further develop your understanding of graphs. Success Criteria: 1) Take the Haribo challenge. 2) Watch a selection of videos about graphs. 3) Answer some practice questions.

How many sweets are in your bag? Record the contents of your bag of sweets by drawing the table below: Do you have a big enough sample to draw any conclusions about the average content of a bag of these sweets? Eggs Hearts Rings Cola bottles Bears Total

Combine the results for the whole class in the table below and work out the mean number of sweets per bag and the mean number of each type of sweet per bag. Eggs Hearts Rings Cola bottles Bears Total Mean=

Using your data Do you now have a big enough sample to draw conclusions from or do you need more results? With sampling remember the Goldilocks principle ‘Not too big, not too small, but just right!’ Calculate the % of each type of sweet per bag. Extension: Sketch a pie chart to show the average distribution of types of sweets in each bag.

Graphs

Graphical Representations You need to know how to present information in a graph. Your data should be easy to read and understand All graphs must be clearly named and have both axis labeled Use an appropriate scale, do not mislead people by using an inappropriate scale (e.g. some political parties do this) Do not draw the raw data – it should be a summary of the data Make sure you use the appropriate graph for the data and not just the one you like

Quick task

Video A quick video about graphs

Remember correlations??? There are three types of correlation… No correlation Positive correlation Negative correlation

Histograms Used to represent data on a ‘continuous’ scale Columns touch because each one forms a single score (interval) on a related scale, e.g., time - number of hours of homework students do each week Scores (intervals) are placed on the x-axis The height of the column shows the frequency of values, e.g., number of students in each interval – this goes on the y-axis

Bar charts Used to represent ‘discrete data’ where the data is in categories, which are placed on the x-axis The mean or frequency is on the y-axis Columns do not touch and have equal width and spacing Examples: Differences in males/females on a spatial task Score on a depression scale before and after treatment

Scattergrams Used for measuring the relationship between two variables Data from one variable is presented on the x-axis, while the other is presented on the y-axis We plot an ‘x’ on the graph where the two variables meet The pattern of plotted points reveals different types of correlation, e.g., positive, negative or no relationship.

Practice exam questions Two groups of patients took part in a trial to compare the effectiveness of two different drug therapies. One of the groups was given Drug A and the other group was given Drug B. All patients completed a rating scale at the start of a ten-week course of treatment and again at the end of the course. This scale measured the severity of symptoms. The Drug A group had an average score of 9 before the therapy and an average score of 4 at the end of the course. The Drug B group had an average score of 7 before the therapy and an average score of 5 at the end of the course. Sketch and label a bar chart to illustrate the data. (4 marks)

Answers

4 marks

Answers 4 marks

4 marks

Answers AO3 = 4 marks The graph shows a strong negative correlation between score on depression scale and weeks of treatment. The more treatments the lower the depression. However, there also seems to be a plateau, where between 2-3.5 weeks there is very little change in depression. 1 mark for each of the following: Strength (it is a moderately strong / strong correlation) Direction (negative) Description of the relationship (the longer the treatment the lower the depression score) Indication of plateau / change in direction.

You will also need to interpret tables

3 marks

Answers AO3 = 3 marks Candidates may point out that the % of secure attachment in all three countries is very similar, but that insecure attachments vary. Country one has the lowest % of insecure-avoidant but the highest of insecure resistant. Country three has the lowest % of insecure-resistant but the highest of insecure-avoidant. One mark for a brief outline of one point. Two further marks for accurate elaboration of one point in detail or more than one point more briefly.

Types of Data Nominal data in categories, e.g. grouping people in class into ‘short’ and ‘tall’, or ‘boys’ and ‘girls’. Ordinal data that is ordered, e.g. lining people up in height order. Interval data measured in equal intervals, e.g. measuring someone’s height or weight. Ratio data with a true zero, e.g. height

Types of Data Nominal data in categories, e.g. grouping people in class into ‘short’ and ‘tall’, or ‘boys’ and ‘girls’. Ordinal data that is ordered, e.g. lining people up in height order. Interval data measured in equal intervals, e.g. measuring someone’s height or weight. Ratio data with a true zero, e.g. height