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Cumulative Frequency A cumulative frequency polygon shows how the cumulative frequency changes as the data values increase. The data is shown on a continuous scale on the horizontal axis. The cumulative frequency is shown on the vertical axis. You plot the upper ends of each group against the cumulative frequency. You then join the points with straight lines.

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Age (years) FrequencyCumulative Frequency 15 to 203 20 to 258 25 to 3017 30 to 3512 35 to 406 40 to 454 Age (years) Cumulative frequency 3 11 28 40 46 50 Age of People in a Survey

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Percentiles and Deciles Percentiles can give information on the spread of the data Take the total cumulative frequency as 100% 10 th Percentile is 10% of the total cumulative frequency 10 th Percentile is also called the 1 st Decile Quartiles split data up into four equal parts, or quarters The Lower Quartile (Q1) is the value one quarter of the way along the data The Median (Q2) is the value one half of the way along the data The Upper Quartile (Q3) is the value three quarters of the way along the data The Inter-Quartile Range is the Upper Quartile minus the Lower Quartile Measures of Spread

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Age (years) FrequencyCumulative Frequency 15 to 203 20 to 258 25 to 3017 30 to 3512 35 to 406 40 to 454 Age (years) Cumulative frequency 3 11 28 40 46 50 Age of People in a Survey Q1 Q2 Q3

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Box and Whisker diagram (Box Plot) Age (years) Cumulative frequency Lower Quartile Upper Quartile Median Lowest Value Highest Value

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Instead of the Whiskers showing the full range of values you only draw the Whiskers: up to the highest value that is not an outlier, and down to the lowest value that is not an outlier Outliers An Outlier may be a value that has been mis-recorded or a value that has been measured and recorded correctly, but does not fall in line with the rest of the data. Outliers are often ignored because they can distort the data. Outliers are values that are unusual in comparison with the rest of the data. To find any outliers you: Find the Inter-Quartile Range (IQR), Lower Quartile (LQ) and Upper Quartile (UQ) Find the value 1.5 times the IQR and subtract from the LQ Find the value 1.5 times the IQR and add to the UQ Any values outside this range are outliers and should be marked on the Box Plot individually

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Cumulative frequency xx Outliers Data: 20, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 28, 29, 30, 30, 30, 34, 38, 40 Lower Quartile = 25 Median = 28 Upper Quartile = 30 Inter-Quartile Range = 5 Outliers: 1.5 times IQR = 7.5, outliers are values higher than 30 + 7.5 = 37.5 (i.e. 38 and 40), and values lower than 25 – 7.5 = 17.5 (none) outliers Lowest Value that is not an outlier Highest Value that is not an outlier

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Section 6.7 Box-and-Whisker Plots Objective: Students will be able to draw, read, and interpret a box-and- whisker plot.

Section 6.7 Box-and-Whisker Plots Objective: Students will be able to draw, read, and interpret a box-and- whisker plot.

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