Maths : Unit 2 by Holly Jones https://padlet.com/hol_cjones/a2767vj57wdl Made with good vibes en-us 2019-01-30 12:12:16 UTC 2023-03-05 15:24:13 UTC hello@padlet.com Scatter Diagrams and correlation hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795218
  • A scatter graph is a useful tool when determining whether a relationship exists between 2 variables
  • It’s usual to draw the independant variable on the horizontal axis and the dependant variable on the vertical axis
    • Correlation 
    • A measure of relationship- the stronger the correlation, the more closely related the variables are likely to be
    • The type of correlation can be described in terms of the gradient of he slope formed by the points and how close the points lie to the straight line
    Correlation Causation
    • Causation - The act or process of causing something
    • Even if there is a correlation within the data, it doesn’t mean that there. Is a direct variable. It could be caused by a third variable

    ]]>     2019-01-30 12:12:27 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795218     Populations and Samples hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795220 Population
    • The total number of things which are available
    Sample
    • Taking a group from the entire population to analyse
    Simple Random Sampling
    • A procedure where every possible element within  a population has an equal chance of being selected, all possible sample groups are equally likely
    • One way to create a random sample it to allocate all elements within the population a number and use a random number generator such as a calculator to produce a random list of values. Select from the population the elements whose value matches those within the random list.
    Systematic Sampling
    • Taking participants from the population at regular intervals, from a list of the whole population
    • To create a systematic sample: determine the number of ‘things’ within the population and the sample size which is required and divide the population by the sample size. Then choose a random starting point and, using the previous value, choose every nth element until the sample is built.
    Opportunity Sampling
    • Samples only from those who are available and willing to take part
    • Care mist be taken as this can introduce bias, especially when groups are small and come from a condensed area
    ]]>     2019-01-30 12:12:27 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795220     Unit 1 hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795221 2019-01-30 12:12:27 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795221 Measures of central tendancy hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795222 Measures of variation
    • Standard Deviation - A measure of how spread out numbers are, units are the same as the original data
    • Variance - The average of the squared difference from the mean
    • Range - Difference between largest and smallest
    • Interquartile range - Upper quartile - lower quartile the spread of the middle 50% of the data
    ]]>     2019-01-30 12:12:27 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795222     Lines hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795223 Line of best fit
    • When a linear relationship exists between two variables, a line of best fit can be drawn
    • It should always pass through the mean point of the graph
    • It can then be used to determine values when another is known
    Regression Lines
    • Another name for a line of best fit calculated mathematically to ensure it produces the most accurate result
    Relationship between the correlation coefficient and description of the data
    r≈ 1 = Strong positive linear correlation
    r≈ 0  = No linear correlation
    r≈ -1 = Strong Negative linear correlation 
    When r = + or - 1, it is perfect correlation; the data lies in a perfectly straight line
    When r=0, there is no linear relationship between the variable
    ]]>     2019-01-30 12:12:28 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795223     Cumulative Frequency hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795224
  • Used to calculate an estimate of the median for a grouped set of data
  • It can also be used to calculate the interquartile range
  • Cumulative frequency is shown along the vertical axis
  • Looks like:
    • ]]>     2019-01-30 12:12:28 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795224     Box and Whisker Plots hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795225 Some sets of data can be summarised using 5 key points:
    1. The median value (Q2) - the middle number once the data has been written in order
    2. Lower Quartile (Q1) - The value which lies one quarter of the way through the ordered data
    3. Upper Quartile (Q3) - The value which lies three quarters of the way through the ordered data
    4. Smallest Value
    5. Largest Value
    The interquartile range is Q3-Q1 and measures the spread of the middle 50% of the data

    ]]>     2019-01-30 12:12:28 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795225     Histograms hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795226
  • A histogram can be used to display grouped continuous data
  • The area of each bar should be in proportion to the frequency 
  • When the class widths are not all equal, proportional areas can be achieved by plotting the frequency density on the vertical axis
  • The class width of an interval is calculated as the difference between the smallest and largest values that could occur in that interval
    • Frequency Density = frequency/class width
    For all histograms remember:
    • Frequency density on the vertical axis
    • Choose suitable scales for axes
    • Label both axes
    ]]>     2019-01-30 12:12:28 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795226     Standard Deviation and Variance hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795227 2019-01-30 12:12:28 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795227 Skewness hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795228 Skewness - Measures the distribution
    Positive Skew - Median is closer to lower quartile
    Negative Skew - Median is closer to upper quartile
    Normal Distribution - Median is near the middle]]>     2019-01-30 12:12:28 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795228     Specification hol_cjones https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795229 2019-01-30 12:12:28 UTC https://padlet.com/hol_cjones/a2767vj57wdl/wish/325795229