34 / 50 Marks The Maths GCSE test scores of 280 students are shown in the histogram below. GCSE_HistogramQuestions. Since there are 30 bags in the 30 – 40 pound category and a further 45 bags in the 40 – 55 pound category, there are 75 bags that have a weight between 30 and 55 pounds. We already know from the previous question that 80 riders rode between 0 and 20 kilometres and that a further 100 riders rode between 20 and 30 kilometres. The easiest thing for us to do is to tabulate our data, with one column for the midpoint of each distance category, another column for the frequency (number of riders) and another column for the midpoint multiplied by the frequency (this last column is to work out the total distance travelled by all the riders in that category combined because to work out the mean, we will need to divide the total distance travelled by all riders by the number of riders). In the 30 – 57 kilometres category, we have a band width of 27 kilometres and a frequency density of 2, so the number of riders can be calculated as follows: In the 57 – 70 kilometres category, we have a band width of 13 kilometres and a frequency density of 9, so the number of riders can be calculated as follows: In the 70 – 90 kilometres category, we have a band width of 20 kilometres and a frequency density of 6, so the number of riders can be calculated as follows: Although we now exactly how many riders rode in each distance category, we cannot know exactly how far each rider rode since we are dealing with grouped data. The key formula when we are dealing with histograms is: If we need to work out the frequency, then we simply need to rearrange this formula: The number of riders (the frequency) who rode between 0 and 20 kilometres can be calculated as follows: The number of riders (the frequency) who rode between 20 and 30 kilometres can be calculated as follows: Therefore the number of riders who rode between 0 and 30 kilometres is: b) In order to work out the mean journey length, we need to work out how many riders there are in total. can be calculated as follows: We can therefore conclude that 15 bags of flour is represented by 75 small squares. Pearson Edexcel Level 1/Level 2 GCSE (9 - 1) GCSE style questions arranged by topic Histograms Taken from the Edexcel 2 year GCSE Scheme of Work, containing prior knowledge, keywords, opportunities for problem solving and common misconceptions. People who can hold their breath for 1 minute or more is represented by the whole of the last bar (70 - 100 seconds) and the right-hand part of the second-to-last bar (60 - 70 seconds). Histograms Practice Questions Click here for Questions . We know from the first question, that 15 bags of flour weigh between 35 and 40 pounds. The height will be on the the x-axis and the frequency density on the y-axis. Histograms look like bar charts but have important differences. Preview. 2. Instructions Use black ink or ball-point pen. pdf, 963 KB. Work out how many people took between 3 and 4 minutes. Model answers & video solution for Histograms. Past paper exam questions organised by topic and difficulty for Edexcel IGCSE Maths. In order to make this work, when drawing a histogram, we plot frequency density on the y-axis rather than frequency. Powerpoint presentation and associated worksheets. A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. Model answers & video solution for Histograms. From 0 to 1 minutes there are 10\times 12 =120 small squares, and from 1 to 1.5 there are 5\times 20=100 small squares (marked on the graph below for clarity). c) What is the median weight of a bag of flour? 40 x KS3 Maths Homework Sheets / Booklet WITH ANSWERS!!!! In a histogram, the area is the important thing. We have made the assumption that the number of bags that weigh between 80 and 95 pounds is \frac{3}{5} of the number of bags of flour that weigh between 70 and 95 pounds. The frequency of the data is measured by area not height. With lengths on the x-axis and frequency density on the y-axis, each bar that we draw will have width equal to its class width, and height equal to the relevant frequency density. Use this quiz to test yourself. b) Find the lower quartile of the scores. …..... (3) … We will therefore need to work out which weight band the 93^{\text{rd}} bag of flour falls into. Covers all types of histogram questions. Histograms. We are now in a position to calculate the estimated weight of the 93^{\text{rd}} bag (this is the hard bit!). If we compare the area to the 30 – 40 pound category, its area is 25 small squares larger than the 30 – 40 pound category. a) The key piece of information in this question is that 15 bags of flour weigh between 35 and 40 pounds. There are many different lengths of routes to suit cyclists of all abilities. (a) Work out an estimate for the number of pigs which weigh more than 80kg. • Keep an eye on the time. The histogram shows information about the weight of the bags of flour: 15 bags of flour weigh between 35 and 40 pounds. ADVANCED CHARTS AND GRAPHS > REVISION > GCSE QUESTIONS. This is illustrated in red on the histogram below. About this resource. Each time you take each quiz you'll be given 10 questions at random. GCSE_HistogramQuestions. The tabulated data should look like the below: The total of the frequency column is the total number of riders. – use this as a guide as to how much time to spend on each question. Histograms On a histogram, the area of the bar , and not the height, represents the frequency of the data . London WC1R 4HQ. Videos, worksheets, 5-a-day and much more Our collection of revision videos on histograms will help: Histogram Revision Videos Your completed histogram should look like the one below: Question 2: Below is a histogram showing how long people can hold their breath. There are no gaps between the bars; It’s the area (as opposed to the height) of each bar that tells you the frequency of that class. Click here for Answers . a) In order to complete the rest of the histogram, we need to work out the frequency densities for the length categories which have not already been drawn on the histogram. Since 5 small squares represents a single bag of flour, then 200 squares represents 40 bags of flour. This carefully selected compilation of exam questions has fully-worked solutions designed for students to go through at home, saving valuable time in class. Example Here is a table of data similar to the last one but with values of height grouped differently using inequalities. Therefore, the number of people who can hold their breath for between 20 and 40 seconds is: Question 3: Some cyclists from a local cycling club go out for their usual Sunday ride. To construct a histogram, we will need the frequency density for each class. KS2/3/4:: Data Handling & Probability:: Data Representation. The area of the 35 – 40 pounds bar (do not accidentally work out the area of the entire 30 – 40 pounds bar!) Exam Questions – Estimating the median from a histogram. The table shows the ages of 25 children on a school trip. Histogram Answers - Displaying top 8 worksheets found for this concept.. What we need to do is look and see what area of the histogram this represents. Since this is half of the total of the 30 – 40 pound category, the number of bags between 30 and 40 pounds is: In the 40 – 55 pound category, the area is 1.5 times the 30 – 40 pound strip, so this represents: So far we have accounted for the first 75 bags of flour (50+75=125) so haven’t reached the 93^{\text{rd}} bag of flour yet. The histogram illustrates the results of the survey. Some of the worksheets for this concept are Work 2 on histograms and box and whisker plots, Histogram work 2013, Histograms multiple choice practice, Box stem leaf histogram work answer key graph it, Histograms, Gcse exam questions on histograms grade aa, Visualizing data date period, Frequency tables and histograms. The histogram below shows this information: a) Estimate the number of cyclists who rode for 30 kilometres or less. b) Explain why your answer or part a) is only an estimate. 1. docx, 615 KB. Worksheet. 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