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Data and Types of Data Qualitative data Quantitative data Discrete data Continuous data Ranked data Bivariate data Rounding and accuracy Definition Data that uses words Data that uses numbers Data that can be counted Data that can be measured Data that has been ranked Data that has two variables Example/ Information Colours, foods, Time, temperature, shoe size Number of siblings Height Definition All the people or objects you are interested in When you collect data from the whole population When you collect data from part of the population Data you collect yourself Notes Ice cream sales and temperature Because continuous data is measured you always have to decide on a level of accuracy, you can use upper and lower bounds to do this Data Collection Term Population Census data Sample Primary data Secondary data Pilot surveys Data that is collected by someone else Is a preliminary survey used to gather information prior to conducting the survey Questionnaires A way of collecting data. Interviews A way of collecting data. Statistical experiments Systematic sampling Stratified sampling Random sampling Quota sampling Cluster sampling Start at a particular point in the data and collect at a regular interval Allows each group within the population to be represented fairly within the population. Allows each person in the population to have an equal chance of being in the sample. The people in the sample just have to be of a particular type. The population is split into smaller group called clusters. One or more clusters is chosen at random. Make sure you know the advantages and disadvantages Make sure you know the advantages and disadvantages Usually used to see if your means of collecting data is going to give you the data you can use to test the hypothesis Check you know how to create questionnaires avoiding bias Make sure you know the advantages and disadvantages Understand how you can use a control group. Use an experiment to predict the whole population Make sure you know the advantages and disadvantages Make sure you know the advantages and disadvantages Make sure you know the advantages and disadvantages Presenting and analysing data You need to be able to construct, use and interpret data in these formats: Tallying / Frequency tables Cumulative frequency tables Cumulative frequency diagrams Cumulative frequency step polygons Two-way tables Pictograms Pie charts Stem and leaf diagrams* Choropleth Maps Bar charts and vertical line charts Misleading diagrams Comparative Pie charts Histograms (frequency density) Frequency Polygons Population Pyramids Skew-ness Averages and measures of spread You need to be able to calculate, use and interpret data with these calculations: Mode, Median, mean of discrete data in lists and in frequency tables Mode, Median, mean of grouped data Which average is best? Transforming data Weighted mean Range Quartiles and inter-quartile range Percentiles and Deciles Box and whisker plots Outliers Standard deviation Standardised scores Scatter diagrams and Correlation You need to be able to construct and interpret a scatter diagram and interpret data: Scatter diagrams Association and Correlation Causal relationships Line of best fit and equation of Interpolation and Extrapolation Spearman’s rank Time Series and index numbers You need to be able to construct, use and interpret data in these formats: Line graphs Time series Trends and trend lines including predictions Seasonal variation and mean seasonal variation Moving averages Index numbers Chain based Index number Weighted based index number Probability and Probability distributions You need to understand all these laws of probability and know the probability distributions: Trails, outcomes and events Sample space Theoretical probability Experimental Probability Mutually exclusive Exhaustive events Independent events Risk insurance Tree diagrams Simulation Venn diagrams Addition law Multiplication law Conditional probability Probability distributions Uniform distributions Binomial distribution Normal distribution Quality assurance Understanding the language on the exam paper When the questions says . . . Calculate. . . Work out or find out. . . Write down. . . It means . . . Some working out is needed – so show it A written mental calculation is needed. Working out is not usually required. You should be able to write down your answer using the information given. Estimate. . . Work out an answer from a table or graph. Estimating means you can not work out an exact value. Diagram NOT accurately Often used for pie charts. Don’t measure angles drawn. . . from the diagram as they will be wrong. You may need to calculate. Give reasons or Explain why. . You need to write an explanation. Show any working out. . Plot . . . Add the points accurately to the graph Draw . . . Use the data to draw an accurate graph or chart Use your graph . . . Read the values from the graph and use them. Predict . . . Use something eg line of best fit to predict. Compare . . . Make any comparisons explicit. It is not enough just to describe the items you are comparing. Explain how they relate to each other.