Exercise 1 – mean/median/mode



Component 1: Research Methods1.3 Data Recording, Analysis and PresentationKnowledge ChecklistPlease tick and date in the box which describes your understanding of the following content. You should be aiming to ensure you can say you fully understand all the content belowContentYES, I FULLY UNDERSTANDI UNDERSTAND SOMEI DO NOT UNDERSTANDTypes of data:QualitativeQuantitativePrimarySecondaryMeasures of Central tendencyMeanModeMedianMeasures of DispersionVarianceRangeStandard DeviationRatioPercentagesFractionsFrequency tablesLine graphPie chartBar chartHistogramsScatter- diagramIf you have ticked the ‘I UNDERSTAND SOME’ or ‘I DO NOT UNDERSTAND’, write below the area in which you do not understand and how you plan on resolving this ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Before we look at data analysis…If you collect data first hand from the sample, like a researcher would from his participant sample, this type of data would be called ____________ data. Whereas, if a researcher used data which was gathered by another researcher this would be called __________________ data.Data Analysis – Descriptive StatisticsDescriptive statistics are ways to summarise and analyse data that has been gathered using a self-report, experiment or observation. Imagine if you’d done a huge study involving hundreds of participants. You couldn’t possibly give an interested party every single score on a test. So we need to summarise the data to make it more understandable so that we can talk about it. Hence we need to describe it, and so we get ‘Descriptive Statistics’.We can do this in a number of ways, and the way/s chosen will depend upon the research method that has been carried out. Think about it: what types of data (results, scores, info etc.) would you expect you’d collect after conducting the research methods available to you as a psychologist. Jot down below:Experiments:Observations:Correlations:Surveys/questionnaires:Case studies/interviews:Types of data - Qualitative dataCase studies/interviews/open-ended questions:These are hard to deal with, as responses are obviously so varied, and somehow you need to categorise or summarise different people’s responses (imagine, you might have an interview transcript (or hundreds!) to deal with). One way of dealing with it is to try and convert it into quantitative data. This is done by grouping responses (say, for an interview) under different categories, once you’ve seen what sort of responses you’ve got. Doing this after the data collection helps to ensure that you minimise the investigator bias. So, for example, you might decide that the main categories are “negative attitude” and “positive attitude” to studying at college. Then you’d have to read through each response and decide what category to put each one in. What could be problematic about doing things this way round?Observations:The same can be said of Observational data. It can also be difficult to analyse unless you have a system. One of the common systems used when analysing observational data is to use a tally chart , where you decide beforehand which categories you are going to look at, and when you see them happen, during your observation sessions, you put ‘a stroke’ in the tally box. Then you can summarise these numerically (quantitatively). You might cover inter-rater reliability here, with your teachers. Ask them!Types of data - Quantitative dataIf we’ve collected quantitative data, or converted previously qualitative data into numerical form, there are a number of major ways we can deal with this formally. These are called MEASURES OF CENTRAL TENDENCY and MEASURES OF DISPERSION. These measures tell us:Measures of central tendency - which figure best represents the group's data (how they are ‘bunched’, centrallyMeasures of dispersion - how widely the scores are spread away from the measures of central tendencyMeasures of Central TendencyThese measures are covered by the calculation of the MEAN, MEDIAN and MODE. Check you know how to calculate them:MEAN:What is it…When would you calculate the mean…MEDIAN:What is it….When would you calculate the median….MODE:What is it….When would you calculate the mode….Exercise 1 – mean/median/modeTry calculating the mean, median and mode of the following sets of data:1,2,3,7,10,20,30,43,47,48,50mean:median:mode:1,2,3,7,10,20,30,43,47,100,600mean:median:mode:1,2,3,4,4,5,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,9,10mean:median:mode:1,30,40,43,45,46,46,46,47,49mean:median:mode:1,30,70,80,85,86,90,100,120,202,500mean:median:mode:Look at the results and try to notice differences about them:what are the differences between data sets in (a) and (b), and what has this done to the m/m/m?what would you say about the m/m/m of (c)?Any other comments about any of the data sets above? Write them below:Exercise 2If you did not have access to the actual raw data above, but were given the measures of central tendency you have worked out, would these measures be a ‘fair’ and ‘reasonable’ description of the complete data? Try comparing the data in (a) and (b) above with their respective measures of central tendency. When is one measure better (more reasonable) than the others?You might have noticed that sometimes one measure is better than the other (contrary to popular belief, the mean is NOT always the best ‘typical’ value; it gets mentioned more often as the layperson’s ‘average’). See if you can list below two advantages and two disadvantages of each measure.AdvantagesDisadvantagesMean12Median12Mode12Measures of DispersionYou may remember that these are descriptions of how widely the data is spread about (is there a wide range of scores?). There are three forms of statistical dispersion: the RANGE, the VARIANCE and the STANDARD DEVIATIONThe RANGE is calculated by subtracting the lowest value in a finding from the highest value in a finding. The VARIANCE is calculated by:Subtracting the central tendency (e.g. mean) from each finding.Squaring these numbers.Finally, calculating the average of all the squared numbers.The STANDARD DEVIATION is calculated by finding the square root of the variance. This tells us how much each score deviates from (or is different from) the mean, and then calculates the mean (average) of all of these deviations. In other words, the SD tells us how far the scores are scattered around the mean.Calculating the range and standard deviationCalculating the range is easy – you take the lowest score from the highest score and add 1 (this last bit seems a bit strange but that’s how it’s done).Example: calculate the range of the scores 2,3,4,4,4,5,5,6,6,6,7,7,8,8,8,8,9,9Answer: 9 minus 2 = 7 + 1 = 8Range = 8Calculating the standard deviation is a little more difficult, but you need to remember that you don’t ever have to do this in an exam. And, you are allowed to use calculators in class! The formula involved takes each score away from the mean and then finds the average (mean) of those differences. Then it square roots the answer. On a calculator you need to find the right mode buttons and then put the data in. The sign for SD is usually ‘theta’ n-1. Your teacher will help you.-12065213995Exercise 3: TOP PRIORITY!Write down below the steps YOU personally have to go through to calculate the SD on YOUR calculator. Do this meticulously and get you neighbour to try it out. You will then have this to refer back to later! 00Exercise 3: TOP PRIORITY!Write down below the steps YOU personally have to go through to calculate the SD on YOUR calculator. Do this meticulously and get you neighbour to try it out. You will then have this to refer back to later! Exercise 4Calculate, using the following data, the m/m/m/r/SD2,3,3,3,3,3,3,4,4,4,4,5,5,6,7,8mean:median:mode:range:SD:2,3,3,3,3,4,5,5,6,6,7,8,8,8,8,9,10mean:median:mode:range:SD:1,2,3,3,4,5,5,6,7,7,8,8,8,8,8,8,9,9,10,10mean:median:mode:range:SD:1,2,3,3,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12,12mean:median:mode:range:SD:1,2,2,3,3,3,4,4,4,4,5,5,5,6,6,7mean:median:mode:range:SD:Now, on some graph paper, draw little histograms of all sets of data above, cut them out and then stick them in the white space adjacent to each data set. Look for patterns in the charts.Other Descriptive StatisticsAlongside the MEAN, the MEDIAN, the MODE, the RANGE, the VARIANCE and STANDARD DEVIATION, there are a number of other descriptive statistics you are expected to be able to deal with. These are as follows:RatiosFractionsPercentagesRATIO is a comparison between values within different categoriesFRACTION is a representation of portions of a whole number calculated by dividing the number on the top by the number on the bottomPERCENTAGES is a fraction in which the common denominator is always 100. The resulting number is followed by the sign %How do you present the data you have collected??In Psychology, there are a number of ways in which you can present data. You may wish to present your data in a FREQUENCY TABLE. A FREQUENCY TABLE is….On the other hand, you may wish to present your data in a graph. There are a number of different types of graphs: LINE GRAPH, PIE CHART, BAR CHART, HISTOGRAM AND SCATTER DIAGRAMS.Exercise 5:You need to know which graph to use and when. To this end, you need to complete the table below:Graph typeSketch oneAppropriate to use when:Not appropriate to use when:Line graphPie chartBar chartHistogramScatter Diagram ................
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