nd for time, weight or height."},{"id":"block-2","content":"Each class interval becomes one point. Plot the class midpoint on the x-axis and the frequency on the y-axis."},{"id":"block-3","content":"Find the midpoint with $\\text{midpoint}=\\frac{\\text{lower end}+\\text{upper end}}{2}$. For $20 < t \\leq 30$, the midpoint is $25$. After plotting all the points, join neighbouring points with straight lines."}]},{"id":"card-2","type":"mcq","order":2,"options":[{"id":"a","text":"$$(20,18)$","isCorrect":false},{"id":"b","text":"$$(25,18)$","isCorrect":true},{"id":"c","text":"$$(30,18)$","isCorrect":false},{"id":"d","text":"$$(25,30)$","isCorrect":false}],"question":"For the class interval $20 < t \\leq 30$ with frequency $18$, which point should be plotted on a frequency polygon?","explanation":"The x-coordinate must be the class midpoint, so you average $20$ and $30$ to get $25$, then use the frequency $18$ as the y-coordinate. A common mistake is A, which uses the lower class end instead of the midpoint.","correctOptionId":"b"},{"id":"card-3","type":"content","order":3,"title":"Worked example: travel times","blocks":[{"id":"block-1","content":"![Frequency polygon for travel times with Time on the horizontal axis and Frequency on the vertical axis showing six plotted points joined by straight lines](https://assets.mathsgenie.co.uk/lesson-v2-img/inline/e4eb3fd0-11e6-4337-9825-b644c2de14f2.jpeg)\n\nA travel-time table has intervals $0 < t \\leq 10$, $10 < t \\leq 20$, $20 < t \\leq 30$, $30 < t \\leq 40$, $40 < t \\leq 50$ and $50 < t \\leq 60$, with frequencies $12, 16, 23, 28, 13$ and $8$. The graph shows the finished frequency polygon for that table."},{"id":"block-2","content":"First find the midpoints: $\\frac{0+10}{2}=5$, $\\frac{10+20}{2}=15$, $\\frac{20+30}{2}=25$, $\\frac{30+40}{2}=35$, $\\frac{40+50}{2}=45$ and $\\frac{50+60}{2}=55$. Then pair midpoint with frequency to get $(5,12)$, $(15,16)$, $(25,23)$, $(35,28)$, $(45,13)$ and $(55,8)$."},{"id":"block-3","content":"Plot the six points carefully on axes labelled Time (minutes) and Frequency. Then join each point to the next with straight line segments, not bars or separate lines to the origin."}]},{"id":"card-4","type":"fill_blank","order":4,"blanks":[{"id":"mid","isMath":true,"correctAnswer":"35"}],"sentence":"For the interval $30 < t \\leq 40$, the midpoint is {{blank:mid}}."},{"id":"card-5","type":"flashcard","cards":[{"id":"fc-1","back":"The number of data values in a class interval.","front":"Frequency"},{"id":"fc-2","back":"A grouped range of values, such as $20 < t \\leq 30$.","front":"Class interval"},{"id":"fc-3","back":"Add the class ends and divide by 2: $\\frac{\\text{lower end}+\\text{upper end}}{2}$.","front":"Midpoint formula"},{"id":"fc-4","back":"A graph made by plotting midpoint-frequency points and joining neighbouring points with straight lines.","front":"Frequency polygon"}],"order":5},{"id":"card-6","type":"content","order":6,"title":"Choosing scales on blank axes","blocks":[{"id":"block-1","content":"Sometimes the grid is blank, so you must choose the scale yourself. Label the x-axis with the variable and units, and label the y-axis Frequency."},{"id":"block-2","content":"The y-axis should usually start at $0$ and extend beyond the largest frequency. The x-axis must use equal steps and include all the midpoints you need to plot."},{"id":"block-3","content":"If all the data values are much larger than $0$, the x-axis does not have to start at $0$. Use sensible jumps such as 5s, 10s or 20s so the graph is easy to read."}]},{"id":"card-7","type":"ordering","items":[{"id":"item-1","content":"Read the grouped table and note the class intervals and frequencies."},{"id":"item-2","content":"Find the midpoint of each class interval."},{"id":"item-3","content":"Choose and label sensible axes that fit the data."},{"id":"item-4","content":"Plot each midpoint-frequency point."},{"id":"item-5","content":"Join neighbouring points with straight line segments."}],"order":7,"instruction":"Put the steps for drawing a frequency polygon in the correct order.","

Frequency Polygons Lesson

Frequency Polygons Lesson