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© Boardworks Ltd 2008 1 of 38 D4 Moving averages and cumulative frequency Maths Age 14-16
© Boardworks Ltd 2008 2 of 38 Contents A A A A A D4.3 Cumulative frequency D4 Moving averages and cumulative frequency D4.5 Box-and-whisker diagrams D4.2 Plotting moving averages D4.1 Moving averages D4.4 Using cumulative frequency graphs
© Boardworks Ltd 2008 3 of 38 Imagine you are going to record how long each member of your class can keep their eyes open without blinking. Choosing class intervals How could this information be recorded? What practical issues might arise? Time is an example of continuous data. You will have to decide how accurately to measure the times: to the nearest tenth of a second? to the nearest second? to the nearest five seconds?
© Boardworks Ltd 2008 4 of 38 You will also have to decide what size class intervals to use. Keeping your eyes open When continuous data is grouped into class intervals it is important that no values are missed out and that there are no overlaps. For example, you may decide to use class intervals with a width of 5 seconds. If everyone keeps their eyes open for more than 10 seconds, the first class interval would be more than 10 seconds, up to and including 15 seconds. This is usually written as 10 < t ≤ 15, where t is the time in seconds. The next class interval would be _________.15 < t ≤ 20
© Boardworks Ltd 2008 5 of 38 Cumulative frequency graph of results
© Boardworks Ltd 2008 6 of 38 Cumulative frequency Cumulative frequency is a running total. It is calculated by adding up the frequencies up to that point. Cumulative frequency 1650 < t ≤ 55 1155 < t ≤ 60 930 < t ≤ 35 1235 < t ≤ 40 2440 < t ≤ 45 2845 < t ≤ 50 Time in secondsFrequencyTime in seconds 89 + 11 = 100 73 + 16 = 89 45 + 28 = 73 21 + 24 = 45 9 + 12 = 21 9 0 < t ≤ 55 0 < t ≤ 60 0 < t ≤ 35 0 < t ≤ 40 0 < t ≤ 45 0 < t ≤ 50 Here are the results of 100 people holding their breath:
© Boardworks Ltd 2008 7 of 38 100 people took part in the experiment. Finding averages using cumulative frequency From the table, how could you find exact values or estimates for: the mean? the mode/ modal group? the median? To find a more accurate value for the median, a cumulative frequency graph can be used. the range?
© Boardworks Ltd 2008 8 of 38 Contents A A A A A D4.4 Using cumulative frequency graphs D4 Moving averages and cumulative frequency D4.5 Box-and-whisker diagrams D4.3 Cumulative frequency D4.2 Plotting moving averages D4.1 Moving averages
© Boardworks Ltd 2008 9 of 38 Cumulative frequency graphs Here is the cumulative frequency table for 100 people holding their breath: Time in secondsCumulative frequency 0 < t ≤ 359 0 < t ≤ 4021 0 < t ≤ 4545 0 < t ≤ 5073 0 < t ≤ 5589 0 < t ≤ 60100 We can plot a cumulative frequency graph as follows:
© Boardworks Ltd 2008 10 of 38 Plotting a cumulative frequency graph Time in seconds Cumulative frequency 30354045505560 10 20 30 40 50 60 70 80 90 100 0 The upper boundary for each class interval is plotted against its cumulative frequency. A smooth curve is then drawn through the points. We can use the graph to estimate the median by finding the time for the 50 th person. This gives us a median time of 47 seconds.
© Boardworks Ltd 2008 11 of 38 The interquartile range Remember; the range is a measure of spread. It is the difference between the highest value and the lowest value. When the range is affected by outliers it is often more appropriate to use the interquartile range. The interquartile range is the range of the middle 50% of the data. The lower quartile is the data item ¼ of the way along the list. The upper quartile is the data item ¾ of the way along the list. interquartile range = upper quartile – lower quartile
© Boardworks Ltd 2008 12 of 38 Finding the interquartile range Time in seconds Cumulative frequency 30354045505560 10 20 30 40 50 60 70 80 90 100 0 The lower quartile is the time of the 25th person. The upper quartile is the time of the 75th person. The interquartile range is the difference between these two values. 51 – 42 = 9 seconds The cumulative frequency graph can be used to locate the upper and lower quartiles, and so find the interquartile range. 42 seconds 51 seconds
© Boardworks Ltd of 38 D4 Moving averages and cumulative frequency KS4 Mathematics.
© Boardworks of 13 Cumulative frequency. © Boardworks of 13 Cumulative frequency tables A cumulative frequency table is used to record the.
How to draw and use….. Cumulative frequency graphs.
© Boardworks Ltd of 38 D4 Moving averages and cumulative frequency Maths Age
CHAPTER 39 Cumulative Frequency. Cumulative Frequency Tables The cumulative frequency is the running total of the frequency up to the end of each class.
Cumulative frequency Constructing a cumulative frequency table Using a cumulative frequency graph to construct a box and whisker diagram.
Cumulative Frequency and Box Plots. Learning Objectives To be able to draw a cumulative frequency curve and use it to estimate the median and interquartile.
© Boardworks Ltd of 49 D2 Averages and range Maths Age
Cumulative frequency Cumulative frequency table Cumulative frequency graph.
Cumulative Frequency Diagrams & Box Plots. Cumulative Frequency Time t minutes 0≤t<55≤t<1010≤t<1515≤t<2020≤t<25 Number of students A group of.
© Boardworks Ltd of 7 This icon indicates the slide contains activities created in Flash. These activities are not editable. For more detailed instructions,
© Boardworks Ltd of 49 D2 Averages and range KS4 Mathematics.
Vocabulary to know: *statistics *data *outlier *mean *median *mode * range.
Starter List 5 types of continuous data List 3 types of discrete data Find the median of the following numbers: 2, 3, 6, 5, 7, 7, 3, 1, 2, 5, 4 Why is.
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Median, Quartiles, Inter-Quartile Range and Box Plots. Measures of Spread Remember: The range is the measure of spread that goes with the mean. Mean =
Do Now Find the mean, median, mode, and range of each data set and then state which measure of central tendency best represents the data. 1)2, 3, 3, 3,
Cumulative Frequency Curves. Outcomes… Calculate the cumulative frequency Write down the upper class boundaries Plot the cumulative frequency curve Find.
GCSE Maths Starter 16 Lesson 16 Frequency polygons (Cumulative frequency H) Mathswatch clip (88[151/152]). To draw a frequency polygon (Grade D ) To.
Do Now: What information can you derive from a box plot? How is that information displayed? Click when ready
Represent sets of data using different visual displays.
10. Presenting and analysing data * Averages for discrete data * Stem and leaf diagrams * Using appropriate averages * The quartiles * Measures of spread.
Quartiles & Extremes (displayed in a Box-and-Whisker Plot) Lower Extreme Lower Quartile Median Upper Quartile Upper Extreme Back.
© Boardworks Ltd of 50 AS-Level Maths: Statistics 1 for AQA These icons indicate that teacher’s notes or useful web addresses are available in the.
YEAR 11 MATHS REVISION Box Plots Cumulative Frequency with Box Plots.
Making a Box & Whiskers Plot Give Me Five!. 5 Numbers are Needed 1) Lowest: Least number of the data set 2) Lower Quartile : The median of the lower half.
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Cumulative Frequency Diagrams & Box Plots OCR Stage 8.
Stem and Leaf Bingo. Pick 8 from the list
Box and Whisker Plots This data shows the scores achieved by fifteen students who took a short maths test. The test was marked out of.
Starter 1.Find the median of Find the median of Calculate the range of Calculate the mode.
Dot Plots & Box Plots ANALYZE DATA In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with.
3:2 powerpointmaths.com Quality resources for the mathematics classroom Reduce your workload and cut down planning Enjoy a new teaching experience Watch.
Click when ready Whiteboardmaths.com © All rights reserved Stand SW 100 In addition to the demos/free presentations in this area there are.
Statistical Inference for Managers Lecture-2 By Imran Khan.
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GCSE Statistics More on Averages. 4.5 Transforming Data GCSE Statistics only Sometimes it is easier to calculate the mean by transforming the data I have.
Cumulative Frequency A cumulative frequency polygon shows how the cumulative frequency changes as the data values increase. The data is shown on a continuous.
Quartiles + Box and Whisker Plots. Quartiles Step 1: Find the Median. This is called Q2, or the second quartile. Step 2: Split the first half into 2 equal.
What is the MEAN? How do we find it? The mean is the numerical average of the data set. The mean is found by adding all the values in the set, then.
© Boardworks Ltd 2001 Statistical Diagrams 2. © Boardworks Ltd 2001 Contents Frequency Polygons Questions6 Key Words 3 Cumulative Frequency Questions.
© Boardworks Ltd of 40 D5 Frequency diagrams for continuous data KS4 Mathematics.
© Boardworks of 15 The range and interquartile range.
1 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt 10 pt 15 pt 20 pt 25 pt 5 pt DefinitionsCalculationsWhat’s.
Box-and-Whisker Plots We have learned various ways of organizing data so far. We have learned –Line graphs –Bar Graphs –Tables Next we will learn Box-and-Whisker.
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Additional Measures of Center and Spread Math Alliance Fall 2011.
Percentiles and Box – and – Whisker Plots Measures of central tendency show us the spread of data. Mean and standard deviation are useful with every day.
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