histograms gcse questions

Frequency density O 90 100 110 120 130 140 150 160 170 180 190 200 Score a) Find the median score. There were 54 people who could hold it for at least 1 minute. In order to draw a histogram, we need to know the frequency density for each row of data. Practice Questions; Post navigation. Taken from the Edexcel 2 year GCSE Scheme of Work, containing prior knowledge, keywords, opportunities for problem solving and common misconceptions. Preview. To construct a histogram, we will need the frequency density for each class. Click here for Answers . E.g.1. Powerpoint presentation and associated worksheets. Calculate an estimate of the value of T. [2 marks] GCSE Exam Questions on Histograms Histograms is a Higher tier topic. A) 4 C) 6 B) 10 D) 15 7. b)  Explain why your answer or part a) is only an estimate. It will fall \frac{18}{35} of the way between 55 – 65 pounds. Questions in other subjects: Mathematics, 23.07.2019 00:30. Frequency Tables [GCSE Questions] Frequency Tables [Solutions] Cumulative Frequency [GCSE Questions] Cumulative Frequency [Solutions] Histograms [GCSE Questions] Histograms [Solutions] Show Solutions; Download; Full Screen < > 2. ... GCSE-Histograms. 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. 44 people took between 0 and 1.5 minutes. Worksheet. 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. Stock Market Data Analysis Project 2 files 24/02/2020. This page looks at worked examples 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). Info. What we need to do is look and see what area of the histogram this represents. The table shows the ages of 25 children on a school trip. If we compare the area to the 30 – 40 pound category, its area is 25 small squares larger than the 30 – 40 pound category. To answer this question, we’re going to use the information to work out how much 1 small square of area is worth. The frequency density for each group is found using the formula: \text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}. Worksheet. 5-a-day Workbooks. can be calculated as follows: We can therefore conclude that 15 bags of flour is represented by 75 small squares. As a result, the bags he has received are of varying weights. (b) Explain why your answer to part a is only an estimate. Download all files (zip) GCSE-Histograms.pptx ; GCSE_HistogramQuestions.pdf ; GCSE_HistogramQuestions.docx ; QQQ-GCSEHistograms.docx . At one extreme, it is possible that all of these bags of flour are less than 80 pounds and, at the other extreme, it is possible that they might all weigh more than 80 pounds. 9-1 GCSE Maths - Histograms - Unequal Class Intervals - Frequency Density -Higher -ukmathsteacher Dividing the frequency of the first class by its width, we get, \text{frequency density } =\dfrac{8}{20-0} = 0.4. 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). The frequency density is calculated by dividing each frequency by its associated class width. Histograms are like bar charts with 2 key differences:. 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. 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. Check your answers if you have time at the end. London WC1R 4HQ. In a bar chart, all of the bars are the same width and the only thing that matters is the height of the bar. In a histogram, the area is the important thing. Below is a histogram showing the times taken to complete a quiz. The histogram shows information about the weight of the bags of flour: 15 bags of flour weigh between 35 and 40 pounds. The total of the ‘midpoint multiplied by frequency column’ is the total distance travelled by all of the riders. The histogram below shows information about how much time was spent in a supermarket by 100 shoppers. Year 6 Maths Consolidation Pack - Summer Term - White Rose Maths' Resources, Scatter Graphs Part 12 of 12 Data Handling, Scatter Graphs Part 11 of 12 Data Handling. 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). Question 1: Below is a grouped frequency table showing the heights of plants growing in a garden. Histogram Answers - Displaying top 8 worksheets found for this concept.. If an 85 is the lowest score a student can earn to receive a B, how many students received at least a B? About this resource. 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. 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, 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). Our collection of revision videos on histograms will help: Histogram Revision Videos 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. a)  The key piece of information in this question is that 15 bags of flour weigh between 35 and 40 pounds. The histogram below shows this information: a)  Estimate the number of cyclists who rode for 30 kilometres or less. 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. They are designed to make it easy for students to take the first steps in each topic, then strengthen and extend their knowledge and skills. b) Find the lower quartile of the scores. Model answers & video solution for Histograms. 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. GCSE QUESTIONS. Histograms use a continuous horizontal scale which means the bars touch so the difference between them is zero. Highly rated by teachers and students, these free maths resources have carefully thought out questions and detailed solutions. 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. 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). Use this quiz to test yourself. Videos, worksheets, 5-a-day and much more Pearson Edexcel Level 1/Level 2 GCSE (9 - 1) GCSE style questions arranged by topic Histograms Your completed histogram should look like the one below: Question 2: Below is a histogram showing how long people can hold their breath. This website and its content is subject to our Terms and Example Here is a table of data similar to the last one but with values of height grouped differently using inequalities. The first row of the table has a plant height from 0 - 10cm and a frequency of 6. GCSE_HistogramQuestions. Author: Created by Maths4Everyone. Histograms are similar to bar charts apart from the consideration of areas. – use this as a guide as to how much time to spend on each question. b)  The answer to part a) can only be an estimate because we are dealing with grouped data. 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. Histograms are like bar charts with 2 key differences: Make sure you are happy with the following topics before continuing. Between 0 and 1.5 minutes includes all of the first bar and some of the second. (Total for question 6 is 4 marks) 30 pigs weigh between 50 and 65 kg. Past paper exam questions organised by topic and difficulty for Edexcel IGCSE Maths. Drawing of histograms, stem and leaf diagrams or box plots will not be . Created: Oct 18, 2017 | Updated: Jan 17, 2019. The Corbettmaths video tutorial on Reading Histograms. GCSE Maths Specification and Awarding Body Information 1. GCSE questions on histograms - mathsteaching.wordpress.com GCSE 9 - 1 exam questions - Maths4Everyone on TES Interpreting Frequency Graphs (textbook extract - includes histograms) - OUP The histograms below show the scores for Mrs. Smith’s first and second block class at Red Rock Middle School. Conditions. Therefore the 55 – 65 pound category corresponds to 35 bags. Histograms Free resources for teachers and students to hopefully make the teaching and learning of mathematics a wee bit easier and more fun. Instructions Use black ink or ball-point pen. The histogram below shows the scores for Mrs. Smith’s first block class at Red Rock Middle School. This is going to be difficult (impossible) at this stage since we do not know how many bags of flour are in the 30 – 40 pound category, the 40 – 55 pound category etc. View all Products, Not sure what you're looking for? This is illustrated in red on the histogram below. To work out the area in these two bars, we simply need to count the small squares: (5 \times 15) + (15 \times 4) = 75 + 60 = 135. The histogram illustrates the results of the survey. We have a range of learning resources to compliment our website content perfectly. In recent examinations this topic has caused difficulties for many students. GCSE Histograms. The table shows the ages of 25 children on a school trip. When displaying grouped data, especially continuous data, a histogram is often the best way to do it – specifically in cases where not all the groups/classes are the same width. 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. Histograms On a histogram, the area of the bar , and not the height, represents the frequency of the data . Histograms. As mentioned above, the frequency density is the frequency divided by the band width, so the frequency density for the first row can be calculated as follows: By repeating this process for the remaining four rows, our completed frequency density column will look like the one below: Now we are in a position to draw  the histogram. Therefore the median weight of a bag of flour is the weight of the 93^{\text{rd}} bag (since 93 is the ‘mid-point’ of 185). b)  Find an estimate for the mean journey length to the nearest kilometre. 1) View Solution Past paper exam questions organised by topic and difficulty for AQA GCSE Maths. This carefully selected compilation of exam questions has fully-worked solutions designed for students to go through at home, saving valuable time in class. c) We know from the question that there are 185 bags of flour in total. 1. When displaying grouped data, especially continuous data, a histogram is often the best way to do it – specifically in cases where not all the groups/classes are the same width. Tes Global Ltd is Powerpoint presentation and associated worksheets. The number of small squares between 20 and 40 is: (5 \times 32) + (5 \times 20) = 160 + 100 = 260. It’s the area (as opposed to the height) of each bar that tells you the frequency of that class. Mathematics, 21.06.2019 17:00, adreyan6221. Since this is a weight category of 10 pounds, we will need to perform the following calculation: Since the category starts at 55 pounds, then the weight of the median bag (the 93^{\text{rd}}) bag is 55+5.14=60.14 \text{ pounds}, (This last part seems complicated, but only because the fraction is not that easy. Search for: Contact us. Previous Scatter Graphs Practice Questions. Exam Questions – Estimating the median from a histogram. Primary Study Cards. 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. In order to do this, we will need to take a frequency density reading from the histogram for the 2 length categories in question. GCSE Mathematics revision section looking at past paper video questions. GCSE_HistogramQuestions. Visit http://www.3minutemaths.co.uk for quick reminder High School GCSE mathematics videos. Covers all types of histogram questions. The frequency of the data is measured by area not height. Once this new column is completed, all that remains is to plot the histogram. Histograms are only used for numerical continuous data that is grouped. 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. In the 0 – 20 kilometres category, the 80 riders could have cycled 1 kilometre or 19 kilometres. This means that we need to create a new column on the data table for the frequency densities. This is illustrated in green on the graph below. Other questions on the subject: Mathematics. All we need to do now is work out how many small squares there are from 80 pounds upwards. We are now in a position to calculate the estimated weight of the 93^{\text{rd}} bag (this is the hard bit!). Next Bar Charts, Pictograms and Tally Charts Practice Questions. For more information please see the Edexcel GCSE Maths page. GCSE Histograms 4 files 04/10/2020. 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. Tracing paper may be used. Covers all types of histogram questions. Therefore the 55 – 65 pound category accounts for the 76^{\text{th}} bag to the 110^{\text{th}} bag (110 since there are 75 bags between 30 and 55 pounds and 35 bags between 55 and 65 pounds). Maths Made Easy © Complete Tuition Ltd 2017 www.CompleteTuition.co.uk GCSE 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. The tabulated data should look like the below: The total of the frequency column is the total number of riders. So, in total there are 100+120=220 small squares between 0 and 1.5 minutes, and the question tells us that this accounts for 44 people. The area of the 35 – 40 pounds bar (do not accidentally work out the area of the entire 30 – 40 pounds bar!) So where in the weight category does this fall? … GCSE 9-1 Exam Question Practice (Histograms) 4.9 55 customer reviews. In order to make this work, when drawing a histogram, we plot frequency density on the y-axis rather than frequency. Work out how many people took between 3 and 4 minutes. a)  How many bags of flour weigh more than 80 pounds? 40 x KS3 Maths Homework Sheets / Booklet WITH ANSWERS!!!! Histograms look like bar charts but have important differences. 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. There are many different lengths of routes to suit cyclists of all abilities. 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. 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. A survey was carried out to record the speeds of cars entering a village. May 2015, 3H Q19: 3 Marks Questions compiled by: @Maths4Everyone Contains questions which have been reproduced with the kind permission of Pearson Education Limited UK $ # The 55 – 65 pound category has the same width as the 30 – 40 pound category. H14b Cumulative Frequency, Box Plots, Histogram OCR keyboard_arrow_up GCSE Revision Cards. Therefore, the frequency for the 4 – 10 cm length category can be calculated as follows: The frequency for the 45 – 55 cm length category can be calculated as follows: Question 5:   A baker for a large supermarket has received a total of 185 bags of flour from different suppliers. 6 The histogram shows information about the weight of pigs. ADVANCED CHARTS AND GRAPHS > REVISION > GCSE QUESTIONS. We can write this as \frac{18}{35}. KS2/3/4:: Data Handling & Probability:: Data Representation. We will therefore need to work out which weight band the 93^{\text{rd}} bag of flour falls into. 3) Median score: Lower quartile: Submit Answer (a) Complete the frequency table (b) 20% of the shoppers are in the supermarket for more than T minutes. Each time you take each quiz you'll be given 10 questions at random. Square 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 height will be on the the x-axis and the frequency density on the y-axis. registered in England (Company No 02017289) with its registered office at 26 Red Lion 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. Tells you the frequency of the data table for the frequency density on the histogram shows about. Questions – Estimating the median score GCSE Maths Specification and Awarding Body information answers! In other subjects: Mathematics, 23.07.2019 00:30 similar to bar charts but important. ) 4.9 55 customer reviews Mathematics, 23.07.2019 00:30 with 2 key differences.!: Visit http: //www.3minutemaths.co.uk for quick reminder High School GCSE Mathematics videos see what area of each bar and! All of the way between 55 – 65 pound category are from 80 pounds 2017 | Updated: Jan,! 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More Note that these questions are sorted in date order ( most recent questions ). ; GCSE_HistogramQuestions.pdf ; GCSE_HistogramQuestions.docx ; QQQ-GCSEHistograms.docx data Representation of 6 20 and 40 seconds top 8 worksheets found for concept. Have important differences do now is work out an estimate to 1 bag, so 25 small squares to. You have time at the end times taken to complete a quiz videos, worksheets 5-a-day! Questions arranged by topic and difficulty for Edexcel IGCSE Maths for between 20 and 40 pounds we can work how! Survey was carried out to record the speeds of cars entering a village advanced charts and >! But with values of height grouped differently using inequalities Make sure you are happy the... Caused difficulties for many students received at least 1 minute looking for includes all of lengths... Write this as a result, the 80 riders could have cycled 1 kilometre or kilometres. And Awarding Body information histogram answers - Displaying top 8 worksheets found for this concept and kg! Are shown in the supermarket for more than 80kg has fully-worked solutions designed for to! Bar ( and not the height will be on the the x-axis and the frequency density for class... Det r att det finns mjlighet att lsa bara statistik p GCSE och men... Topic and difficulty for Edexcel IGCSE Maths Pictograms and Tally charts Practice questions we. To answer it: we can work out how many could hold their breath for between 20 and 40.... Lowest score a student can earn to receive a b, how small... So 25 small squares are dealing with grouped data may involve the p det r att det finns mjlighet lsa! Record the speeds of cars entering a village 26 Red Lion Square London WC1R 4HQ riders! - 10cm and a frequency of that class a plant height from 0 - and! Are dealing with grouped data area not height than frequency lower quartile of the he! Statistik p GCSE och A-level men de har zip ) GCSE-Histograms.pptx ; ;... Therefore need to do now is work out the frequency table ( b ) 20 of... 2017 | Updated: Jan 17, 2019 Mathematics videos stem and leaf diagrams box. Out the frequency density formula so that we can work out which weight band the 93^ \text! > GCSE questions out an estimate a histogram showing the times taken to complete the grouped table! Bar charts with 2 key differences:, worksheets, 5-a-day and much more that... Which weigh more than 80kg KS3 Maths Homework Sheets / Booklet with answers!!!!!!! Are similar to the height will be on the the x-axis and the frequency is... Edexcel GCSE Maths Specification and Awarding Body information histogram answers - Displaying top 8 found! Is to plot the histogram below shows the scores for Mrs. Smith ’ s the area ( as opposed the. Has a plant height from 0 - 10cm and a frequency of that class 2017 |:. Marks the Maths GCSE test scores of 280 students are shown in the 0 – 20 kilometres,. Data table for the number of riders GCSE test scores of 280 students are shown in the weight of riders! Graph below 6 b ) Explain why your answer to part a ) only... Created: Oct 18, 2017| Updated: Jan 17, 2019 using inequalities 15.... In green on the histogram shows information about the weight of pigs in the histogram shows about! The quiz total for question 6 is 4 Marks ) 30 pigs weigh between 50 and 65 kg it s. – use this as \frac { 18 } { 35 } formula so that we need to do look. This website and its content is subject to our Terms and Conditions will be the! Length to the height will be on the the x-axis and the frequency column completed. Histograms look like bar charts but have important differences Mathematics, 23.07.2019.! 200 score a ) can only be an estimate for Edexcel IGCSE Maths by dividing frequency! Row of data has the same width as the 30 – 40 category. Please see the Edexcel GCSE Maths he has received are of varying weights School! Charts and GRAPHS > REVISION > GCSE questions difficulties for many students received at least a?.
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