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Wynberg girls high-Jade Gibson-maths-data analysis statistics

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Powerpoint slides for data analysis in statistics

Powerpoint slides for data analysis in statistics

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  • 1. Data Analysis Chapter 10
  • 2. Types of Data
    • Quantitative data is data recorded with numbers
      • eg: learner’s weight or number of goals
    • Qualitative data is data recorded in words
      • eg: favourite colours
  • 3. … types of data cont.
    • Within these two types of data we can also look at …
      • Discrete data – information collected by counting (1, 2, 3 … no halves/quarters etc)
      • Continuous data – information collected by measurement (may have decimals and fractions)
      • Do Ex 10.8 Q1 (Pg 232)
  • 4. Data Interpretation
    • Once data has been collected and sorted, it has to be interpreted and analysed
    • Two types of interpretation:
      • Pictorial methods: involve drawing graphs
  • 5.
      • Arithmetic methods: involve working out:
        • Measures of central tendency – mean median and mode
        • Measure of dispersion – range, percentiles, quartiles and the interquartile range
  • 6. Displaying data (Pictorial methods)
    • Histograms – no gaps (quanitative data)
    • Bar Graphs – bars do not touch
    • Compounded bar graphs
      • Dual bar graph – data displayed next to each other
      • Sectional bar graph – data displayed ‘on-top of one another’
    • Pie Charts
    • Broken line graphs
  • 7. Ex. 10.2 (3)
  • 8. 10.3 (1)
  • 9. 10.4 (2)
  • 10. Misleading graphs
    • Ways graphs/charts can be misleading:
      • Using 3D in pictograms/bar-charts
      • Using perspective/shape to exaggerate
      • Reversing the direction of an axis (to make a decrease seem like an increase)
      • Altering the scale of the y-axis (to make it look more or less steep)
      • Leaving part of the axis out to exaggerate differences
      • http://www.coolschool.ca/lor/AMA11/unit1/U01L02.htm#
  • 11. Misleading statistics
    • Stats are notorious for being made up or misleading
    • E.g.: during a political debate in USA , a member of the opposition claimed that employment had gone up during the President’s term of office; yes it had … but only because the population had increased, the number of unemployed people had also increased.
  • 12.
    • “ 86 % of statistics are made up on the spot and the remaining 24% are flawed”
  • 13. Measures of central tendency
    • Mean, mode and median
    • “Averages”
  • 14.
    • Mean (x) is like the average:
      • Mean = sum of values
          • number of values
      • Can be affected by outliers, so not a good measure of central tendency if outliers
  • 15.
    • Median is the one in the middle when placed in numerical order (smallest to biggest)
      • If there are outliers then median is a better measure of central tendency
    • Mode/Modal value is the value that appears the most
  • 16. Things which can help with measures of central tendency
    • Frequency tables
      • Simple tables
      • Or for grouped data
    • Stem and Leaf diagrams – these are especially helpful for data with more than ten items
  • 17. 10.9 (3) 5 19 8, 6, 3 20 7, 5, 5, 4, 0 0, 0 18 9, 9, 4 6, 6, 8, 8 17 9, 6, 3 2, 4, 5, 5, 7 16 0 6, 8, 8, 8 15 5, 1, 0 14 9, 6 13 9 12 4 11 0, 8 10 Robert Jabu Heights of mealie plants (in cm)
  • 18. 10.10 (1) 9 2 0 9 0 10 0, 2, 2, 7 8 0, 2, 7, 8, 9 7 4, 5, 9 6 0, 1, 2, 2, 2, 4, 4, 6, 9, 9 5 4, 5, 5, 5, 5, 7, 7 4 2, 6, 9 3 Leaves Stem
  • 19. Grouped data
    • When the data has many different measurements involved in it, the data is usually grouped in intervals (classes). Try to have between 8 and 14 classes. And start with a value below the minimum in the data.
    • Tally : lines used to count up the frequency of scores
    • Frequency is the number of times that score/value appears
  • 20. Example of a ‘Grouped data table’
    • Midpoint is the midpoint of that interval; calculated as on the table above
    • fX = frequency multiplied by midpoint
    48 8 6 //// / 6-10 9 (1+5) ÷2= 3 3 /// 1-5 fX (Frequency x midpoint) Midpoint (X) Frequency (f) Tally Classes
  • 21. Analysing the grouped data
      • We can calculate:
        • Actual mean (x) = sum of values
        • number of values
        • Estimated mean (X) = sum of ‘fX’ values
            • number of values
      • We can draw a graph using the data:
        • eg: a histogram with ‘classes’ on the x-axis and ‘frequency’ on the y-axis
  • 22.
      • We can find both a mode and modal class:
        • Mode: value that appears most
        • Modal class: class (interval) with highest frequency
      • We can estimate the median from a histogram:
        • By estimating the value at which the ‘area’ of the histogram is divided into two equal parts
  • 23. Histograms and frequency polygons
    • Histograms and frequency polygons are both ‘frequency graphs’
      • The difference between them is that the histogram is made up of bars, whereas the frequency polygon is a line graph
      • The ‘polygon’ is made from the lines of the graph and the horizontal axis
  • 24. Drawing Frequency Polygons (2 methods)
    • 1) Using the bars of a histogram
      • Mark the midpoint of the top of each bar
      • Join the points; including two points at zero on either side of the histogram
  • 25.
    • 2) Without using a histogram:
      • Plot the midpoint of each interval against the frequency
      • Join the points; and add the two “zero” points on either side as with the histogram
  • 26. Measures of Dispersion
    • Tell us how the data is grouped around the “average”
    • Is it closely grouped, or scattered widely?
    • Measure of spread, scattering or dispersion of scores
  • 27. Range
    • Range = largest value – smallest value
      • Has a few limitations in that it cannot be used for ‘grouped data’; and it doesn’t tell us anything about the distribution of the values between the largest and smallest
      • For this reason we can also look at quartiles, deciles and/or percentiles
  • 28. Quartiles, Percentiles and Deciles
    • Quartiles : are points that subdivide the data into quarters
    • Deciles : are points that subdivide the data into tenths
    • Percentiles : are points that subdivide the data into hundredths
  • 29. Quartiles
    • First/lower quartile (Q 1 ) : is one quarter of the way through the data set when ordered from lowest to highest
    • Second quartile (Q 2 ) = median
    • Third/upper quartile (Q 3 ) : is three quarters of the way through the data set (in order)
  • 30.
    • Interquartile range = third quartile – first quartile
    • The interquartile range is a better measure of dispersion than the range as it is not affected by ‘extreme’ values
    • It indicates how densely the data is spread around the median
  • 31.
    • Semi-quartile range = Q 3 – Q 1
            • 2
    • It is half of the interquartile range

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