Skills test Numeracy support

Reading and interpreting data Finding percentages Averages (including mean, median and mode) Range Box and whisker plots identify trends correctly make comparisons in order to draw conclusions interpret information accurately Scatter diagrams L Greenwood March 2018

Nearest whole number means Answer to a calculation is 28.875 The question asks you to give your answer to the nearest whole number. The answer that you have worked out is between 28 and 29, so you need to decide whether to round down to 28 or round up to 29. To do this, look at the digit immediately to the right of the decimal point. If the digit is a 5 or above then you round up. If it is a 4 or below then you need to round down. In this case the digit immediately after the decimal point is a 8, so you need to round up to 29. 5+ 4-

Finding percentages At a staff meeting, the head teacher presented the following table, showing the number of pupils in each class in a school who are having extra music lessons. What percentage of pupils in the school are having extra music lessons? Give your answer to the nearest whole number. Answer: _______________ % So 44 out of 210 are having music lessons. So we type into the calculator 44 ÷ 210 = 0.209 To find a percentage we need to multiply it by 100. 0.209 x 100 = 20.9 First we need to find out how many pupils are having extra music lessons total = 44 Next we need to find out how many children there are in total in the school =use the calculator = 210 210 44 The question asks us to give the answer to the nearest whole number so we need to round this answer up to 21 21 L Greenwood March 2018

Box and Whisker plots What you need to know? •How to read values from a box and whisker plot. •How to compare data from two or more box and whisker plots. •How to work out the quantity represented by each section of a box and whisker plot

L Greenwood March 2018

A teacher presented the following box-and-whisker diagram as part of a staff discussion on pupils' performance. The diagram shows the percentage test marks in mathematics for a revision test for two class groups. Tick all the true statements: The range of percentage marks was greatest in Class A. The median percentage mark in Class A was 15 percentage points less than the median percentage in Class B. The interquartile range was the same in both classes. True - Class A range is 30 (60-30) and Class B range is 60-35 = 25 False – Median for class A = 45 Median for class B = 50 - difference of 5% points True – interquartile range for A is 10 (40-50) and for B is 10 (45-55) L Greenwood March 2018

Scatter diagrams To inform her choice of reading materials, a primary teacher looked at the spread of reading ages in her class. The scatter graph shows the actual age and reading age of 21 pupils in the class. What is the range of reading ages for the pupils in the class? 13 months 19 months 21 months The range is from the lowest point – 5 yrs. 10 months to the highest point – 7 yrs. 7 months = 21 months First black arrow emphasises that we are looking at the reading ages for this question – and the graphs goes up in months The bottom clack arrow shows the lowest reading age (5 years and 10 months) and the arrow at the top point to the two children who both achieved the highest reading age – 7 years 7 months L Greenwood March 2018

Count up the red squares that are ON the line Scatter diagram 2 To inform her choice of reading materials, a primary teacher looked at the spread of reading ages in her class. The scatter graph shows the actual age and reading age of 21 pupils in the class. What proportion of the class have the same reading age as their actual age? Give your answer as a decimal to one decimal place. Count up the red squares that are ON the line This blue line shows us children who have the same reading age as their actual age 6 21 = 6 ÷ 21 Use a calculator to find the answer 6 children are on the line So to find the proportion we are comparing the number of children on the line to the total number of children = 6 out of 21. As we have to give the answer to one decimal place then we have to divide 6 by 21 = 0.2857 Proportion means 6 out of a total 21 ANS = 0.285 Which is 0.3 to one decimal place L Greenwood March 2018

Cumulative frequency curve A cumulative frequency curve is constructed from a cumulative frequency table What You Need to Know How to interpret cumulative frequency tables. How to read values from a cumulative frequency graph. How to find 'more than' values from a cumulative frequency graph. How to find medians, quartiles and interquartile range from a cumulative frequency graph. L Greenwood March 2018

Cumulative frequency graphs Key idea They all look similar and start on the bottom left and go up to the top right because it is a CUMULATIVE frequency graph. We are adding together our frequencies as we go. Each point includes values from the point before. This chart looks at the number of marks the students got in a test So 1 pupil scored between 0-10 marks This point shows the number of pupils who scored 10 marks or less ≤ 10 1 L Greenwood March 2018

Cumulative frequency graphs Score Cumulative total Number of pupils ≤ 10 1 0-10 ≤ 20 2 11-20 This chart looks at the number of marks the students got in a test So in total there are 2 pupils, 1 who scored 0-10 1 who scored 11-20 This 2 also included the one who got 0-10 This point shows the number of pupils who scored 20 marks or less ≤ 20 2 L Greenwood March 2018

Cumulative frequency graphs Score Cumulative total Number of pupils ≤ 10 1 0-10 ≤ 20 2 11-20 ≤ 30 4 21-30 This chart looks at the number of marks the students got in a test So in total there are 4 pupils, 1 who scored 0-10 1 who scored 11-20 2 who scored 21-30 This 4 also included the two who got 0-20 This point shows the number of pupils who scored 0 marks or less ≤ 30 4 L Greenwood March 2018

9 How many pupils scored 50 marks or less? Cumulative total Number of pupils ≤ 10 1 0-10 ≤ 20 2 11-20 ≤ 30 4 21-30 24 How many pupils scored 50 marks or less? 9 How many pupils scored 31- 50 marks? 9 – 4 = 5 How many pupils scored more than 50 marks? 24 – 9 = 15 L Greenwood March 2018

Interpreting cumulative data True or False False – one pupil scored more L Greenwood March 2018

Interpreting cumulative data 24 True or False The question asks if the difference is 10. We can see the difference is 55-60 which is a difference of 5. SO the answer is FALSE! 12 The median score for the non-calculator paper is 55 And the median score for the calculator paper is 60 False – one pupil scored more The median score is the middle score. 24 people took the test so the middle would be 12 L Greenwood March 2018

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