Dot Plot Dot plots show data is distributed
Dot Plot Dot plots show data is distributed (spread out) using a number line.
Example : A group of students measure their pulse rates when resting. The rates are 66, 69, 62, 58, 74, 56, 67, 72, 61, 62, 59 What can you say or 1. Lowest value is 56 BPM work out from this 2. Highest value is 74 BPM data? 3. Mode is 62 BPM 4. Median is also 62 BPM 5. Distribution is flat 50 60 70 80
By looking at thefor shape of the Common expressions various dot plots. distribution try to describe the six possible types. Symmetrical distribution Uniform distribution Skewed right distribution Wide spread distribution Tightly clustered distribution Skewed left distribution
Five Figure Summary When a set of numbers are put in ORDER, it can be summarised by quoting five figures. 1. The highest number (H) 2. The lowest number (L) 3. The median, the number that halves the list (Q 2) 4. The upper quartile, the median of the upper half (Q 3) 5. The lower quartile, the median of the lower half (Q 1)
Five Figure Summary Example Find the. Qfive figure summary for the data. 2 = Median Q = lower Q 3 =9, upper (middle value) 2, 4, 5, 5, 6, 7, 7, 7, 8, 10 middle value 1 middle value The 11 numbers are already in order ! Q 1 = 5 Q 2 = 7 Q 3 = 8 2 L =2 4 5 5 6 7 7 7 8 9 10 H = 10
Five Figure Summary Example Find the. Qfive figure summary for the data. = Median 2 Q 1 = lower 2, middle value 4, (middle 5, 5, value) 6, 7, 7, 8, Q 9, 10 3 = upper middle value The 10 numbers are already in order ! Q 1 = 5 2 L= 2 4 5 Q 2 = 6· 5 5 6 7 Q 3 = 8 7 8 9 10 H = 10
Five Figure Summary Example Find the five figure summary for the data. Median 6, 7, 8, 9, 10 2 = 5, Q 1 = lower 2, 4, Q 5, Q = upper middle value Q 3 = upper middle value (middle value) The 9 numbers are already in order ! Q 1 = 4· 5 2 L= 2 4 5 Q 2 = 6 5 6 Q 3 = 8· 5 7 8 9 10 H = 10
Averages (The Median) The median is the middle value of a set of data once the data has been ordered. Example 1. Tim hit 12 balls at Grimsby driving range. The recorded distances of his drives, measured in yards, are given below. Find the median distance for his drives. 85, 125, 130, 65, 100, 75, 50, 140, 135, 95, 70 50, 65, 70, 75, 85, 95, 100, 125, 130, 135, 140 Two middle values so take the mean. Order the data Median drive = 90 yards
Finding the median, quartiles and inter-quartile range. Example 1: Find the median and quartiles for the data below. 12, 6, 4, 9, 8, 5, 9, 8, 10 Order the data Q 1 Q 2 4, 4, 5, 6, 8, 8, 8, 9, Lower Quartile = 5½ Median =8 Q 3 9, 9, 10, 12 Upper Quartile =9 Inter- Quartile Range = 9 - 5½ = 3½
Finding the median, quartiles and inter-quartile range. Example 2: Find the median and quartiles for the data below. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10 Order the data Q 1 Q 2 3, 4, 4, 6, 8, 8, 8, 9, Lower Quartile = 4 Median =8 Q 3 10, 15 Upper Quartile = 10 Inter- Quartile Range = 10 - 4 = 6
Box and Whisker Diagrams. Box plots are useful for comparing two or more sets of data like that shown below for heights of boys and girls in a class. Anatomy of a Box and Whisker Diagram. Lowest Value 4 Lower Quartile Whisker 5 Upper Median Quartile Box 6 7 8 9 Highest Value Whisker 10 11 12 Boys 130 140 150 160 170 180 Girls 190
Drawing a Box Plot. Example 1: Draw a Box plot for the data below Q 2 Q 1 Q 3 4, 4, 5, 6, 8, 8, 8, 9, Lower Quartile = 5½ 4 5 9, 9, 10, 12 Upper Quartile =9 Median =8 6 7 8 9 10 11 12
Drawing a Box Plot. Example 2: Draw a Box plot for the data below Q 1 Q 2 Q 3 3, 4, 4, 6, 8, 8, 8, 9, Lower Quartile =4 3 4 5 Upper Quartile = 10 Median =8 6 7 8 10, 15, 9 10 11 12 13 14 15
Drawing a Box Plot. Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data. Q 2 Q 1 Q 3 137, 148, 155, 158, 165, 166, 171, 173, 175, 180, 184, 186 Lower Quartile = 158 130 140 Upper Quartile = 180 Median = 171 150 160 170 180 190
Drawing a Box Plot Question: Gemma recorded the heights in cm of girls in the same class and constructed a box plot from the data. The box plots for both boys and girls are shown below. Use the box plots to choose some correct statements comparing heights of boys and girls in the class. Justify your answers. Boys 130 140 150 160 170 180 Girls 1. The girls are taller on average. 2. The boys are taller on average. 3. The girls show less variability in height. 5. The smallest person is a girl 4. The boys show less variability in height. 6. The tallest person is a boy 190
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