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# histograms gcse questions

KS2/3/4:: Data Handling & Probability:: Data Representation. Created: Oct 18, 2017| Updated: Jan 17, 2019, This carefully selected compilation of exam questions has. In a histogram, the area is the important thing. pdf, 963 KB. Between 80 and 95 pounds there are 75 small squares, and between 95 and 100 pounds, there are a further 125 small squares, giving us a total of 200 small squares. Work out how many could hold their breath for between 20 and 40 seconds. The histograms below show the scores for Mrs. Smith’s first and second block class at Red Rock Middle School. Histograms are similar to bar charts apart from the consideration of areas. The histogram below shows information about how much time was spent in a supermarket by 100 shoppers. Author: Created by Maths4Everyone. This carefully selected compilation of exam questions has fully-worked solutions designed for students to go through at home, saving valuable time in class. Histograms are only used for numerical continuous data that is grouped. Therefore, 1 person is equal to, Now, reading from the graph we get that there are 11 \times 10 = 110 small squares between 3 and 4 minutes, so given that 5 small squares is one person, there must be. The table shows the ages of 25 children on a school trip. 1. Model answers & video solution for Histograms. We have been told that 54 people can hold their breath for at least a minute, so this means that the area of the bars from 60 seconds upwards represents 54 people. The area of the 35 – 40 pounds bar (do not accidentally work out the area of the entire 30 – 40 pounds bar!) Below is a grouped frequency table of the lengths of 71 pieces of string. Stock Market Data Analysis Project 2 files 24/02/2020. The number of small squares between 20 and 40 is: (5 \times 32) + (5 \times 20) = 160 + 100 = 260. Reading from the histogram, we see that the frequency density for the 4 – 10 cm category is 3.5, and the frequency density for the 45 - 55 cm category is 4.6. Exam Questions – Estimating the median from a histogram. 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). Once we have calculated the frequency density with the remaining groups, then it is good to add a third column to the table containing the frequency density values, see the completed table. 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. The 55 – 65 pound category has the same width as the 30 – 40 pound category. Covers all types of histogram questions. Histograms Practice Questions Click here for Questions . What we have to do is assume that the distance that each cyclist rode is the midpoint of each distance category (this is why this is an estimated mean and not an accurate mean). The Corbettmaths video tutorial on Reading Histograms. c)  What is the median weight of a bag of flour? In order to draw a histogram, we need to know the frequency density for each row of data. Histograms are like bar charts with 2 key differences:. The histogram shows information about the weight of the bags of flour: 15 bags of flour weigh between 35 and 40 pounds. Created: Oct 18, 2017 | Updated: Jan 17, 2019. We have a range of learning resources to compliment our website content perfectly. The table shows the ages of 25 children on a school trip. Below is a histogram showing the times taken to complete a quiz. Next Bar Charts, Pictograms and Tally Charts Practice Questions. b)  The answer to part a) can only be an estimate because we are dealing with grouped data. Worksheet. Histograms. If 135 small squares represents  54 people, we can work out how many people one small square represents: Now that we know that 1 person is represented by 2.5 small squares, we need to work out how many small squares there are between 20 and 40 seconds. H14b Cumulative Frequency, Box Plots, Histogram OCR keyboard_arrow_up Practice Questions; Post navigation. Histograms is a Higher tier topic. Histograms On a histogram, the area of the bar , and not the height, represents the frequency of the data . Previous Scatter Graphs Practice Questions. Tes Global Ltd is GCSE Maths Specification and Awarding Body Information In the 0 – 20 kilometres category, the 80 riders could have cycled 1 kilometre or 19 kilometres. View all Products, Not sure what you're looking for? The histogram illustrates the results of the survey. If there were 20 bags in the 55 – 65 pound category, and it was the 10^{\text{th}} bag in this category that represented the median, since the 10^{\text{th}} bag in the category is exactly half way through the 20 bags in the category, then its estimated weight would simply be half way between 55 and 65 pounds, so would therefore have a weight of 60 pounds.). This means that we need to create a new column on the data table for the frequency densities. Tracing paper may be used. Past paper exam questions organised by topic and difficulty for Edexcel IGCSE Maths. 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. Dividing the frequency of the first class by its width, we get, \text{frequency density } =\dfrac{8}{20-0} = 0.4. The total of the ‘midpoint multiplied by frequency column’ is the total distance travelled by all of the riders. A project ended for higher-ability GCSE students that (a) gives a basic overview of financial markets (b) introduces important spreadsheet skills and (c) tasks students with analysing stock market data and comparing to conventional savings accounts. In order to make this work, when drawing a histogram, we plot frequency density on the y-axis rather than frequency. Past paper exam questions organised by topic and difficulty for AQA GCSE Maths. b)  Find an estimate for the mean journey length to the nearest kilometre. E.g.1. London WC1R 4HQ. 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. Videos, worksheets, 5-a-day and much more 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). To construct a histogram, we will need the frequency density for each class. This page looks at worked examples for Histograms. a)  Since we are taking data from the histogram, we can see the frequency density and the band width, but we need to work out how many riders (the frequency) rode for 30 kilometres or less. The number of values in each class is represented by the area of each bar (and not the height). Visit http://www.mathsmadeeasy.co.uk/ for more fantastic resources. Powerpoint presentation and associated worksheets. Therefore, once we know what an area of 25 small squares represents, we can add this to 30 (the number of bags represented by the 30 – 40 pound category). The height will be on the the x-axis and the frequency density on the y-axis. Once this new column is completed, all that remains is to plot the histogram. Since the band widths are not consistent (the band width of the 20 - 24 cm category is only 4 cm whereas the band width for the 30 - 50 cm category is 20 cm), this means that the widths of the bars you draw will not be the same. Read our guide, \text{Frequency density} = 6 \div10 = 0.6, 54\text{ people} = 135\text{ small squares}, \text{1 person } = \dfrac{135}{54} = 2.5\text{ small squares}, \text{Frequency density} = \dfrac{\text{frequency}}{\text{bandwidth}}, \text{Frequency} = \text{ frequency density}\times\text{ bandwidth}, \text{Estimated mean} = 22678.5\text{ kilometres} \div \text471\text{ riders} \approx 48\text{ kilometres}, \text{Frequency density} =  32 \div 4 = 8, \text{Frequency density} =  22 \div 10 = 2.2, \text{Frequency density} =  42 \div 20 = 2.1, \text{Frequency density} =  30 \div 5 = 6, \text{Frequency density} =  9 \div 15 = 0.6, \text{Frequency} =\text{frequency density}\times\text{bandwidth}, 2.5\times30\text{ small squares} = 75\text{ small squares}, 15\text{ bags} = 75\text { small squares}, \dfrac{18}{35}\times10=5.14\text{ pounds}. 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. We are trying to locate the weight of the 93^{\text{rd}} bag, so we know it must be in the 55 to 65 pound weight category. 3) Median score: Lower quartile: Submit Answer Pearson Edexcel Level 1/Level 2 GCSE (9 - 1) GCSE style questions arranged by topic Histograms The frequency density for each group is found using the formula: \text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}. GCSE_HistogramQuestions. Click here for Answers . Search for: Contact us. In a histogram, there are no gaps between the bars; the area of each bar is proportional to the frequency; So, a histogram must be constructed so that the area of a bar is proportional to the frequency. Edexcel GCSE Mathematics (Linear) – 1MA0 HISTOGRAMS Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Therefore the estimated mean can be calculated as follows: Question 4: The table shows information about the length of fish caught by some fisherman at a local lake: a)  Use the information on the table to complete the histogram: b)  Use the histogram to complete the table above. Instructions Use black ink or ball-point pen. GCSE Revision Cards. 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. Histograms look like bar charts but have important differences. This website and its content is subject to our Terms and A histograms is a form of bar chart; however, there are two main differences. 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. 40 x KS3 Maths Homework Sheets / Booklet WITH ANSWERS!!!! Since 5 small squares represents a single bag of flour, then 200 squares represents 40 bags of flour. A) 4 C) 6 B) 10 D) 15 7. 1) View Solution Mathematics / Data and statistics / Data processing, Mathematics / Data and statistics / Data representation, Mathematics / Data and statistics / Handling data, GCSE 9-1 Exam Question Practice (Vectors), GCSE 9-1 Exam Question Practice (Trigonometry), GCSE 9-1 Exam Question Practice (3D Pythagoras + Trigonometry). Your completed histogram should look like the one below: Question 2: Below is a histogram showing how long people can hold their breath. How to draw a histogram from some grouped frequency data is covered first, then how to use a histogram to answer questions about the data. docx, 615 KB. A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. There were 54 people who could hold it for at least 1 minute. • Keep an eye on the time. Preview. In order to do this, we need to work out how many riders rode between 0 – 20 kilometres, 20 – 30 kilometres, 30 – 54 kilometres etc. 34 / 50 Marks The Maths GCSE test scores of 280 students are shown in the histogram below. The resources include revision questions for KS2 SATs and GCSE. There are many different lengths of routes to suit cyclists of all abilities. ... GCSE-Histograms. 44 people took between 0 and 1.5 minutes. The frequency density for the 0 – 4 cm length category can be calculated as follows: The frequency density for the 10– 20 cm length category can be calculated as follows: The frequency density for the 20 – 40 cm length category can be calculated as follows: The frequency density for the 40 – 45 cm length category can be calculated as follows: The frequency density for the 55 – 70 cm length category can be calculated as follows: Now that we have worked out the frequency density for each length category, we can now plot them on the histogram, with a result similar to the below: b)  For this part of the question, we need to fill in the gaps in the frequency column of the table. 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. To plot the histogram this represents ) 6 b ) Explain why answer! 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And 1.5 minutes includes all of the second first bar and some of way... Height ) of each bar that tells you the frequency density for each class frequency.. ) 10 D ) 15 7 worksheets found for this concept ) D... Are two main differences Make this work, when drawing a histogram, we need! Rearrange the frequency table of data: we can write this as \frac { }... Plots will not be of the shoppers are in the supermarket for more than 80 pounds Awarding!, then 200 squares represents a single bag of flour in total time in class the... The ‘ midpoint multiplied by frequency column histograms gcse questions is the median score GCSE. But with values of height grouped differently using inequalities and some of the he. ; GCSE_HistogramQuestions.pdf ; GCSE_HistogramQuestions.docx ; QQQ-GCSEHistograms.docx 2017| Updated: Jan 17, 2019, this carefully selected compilation of questions!