StatisticsScatter diagrams
Loading original question
1 “We eat more ice cream as the temperature rises.” What type of correlation is this? ................................................... [1]
IGCSE Mathematics 0580 · Topic practice
Practise averages, charts, cumulative frequency, histograms and scatter diagrams. Read the axes and scales carefully before you calculate or interpret anything.
Appears inPaper 1 64Paper 2 84Paper 3 57Paper 4 81
You’re practising 2016–2018 papers. The 2019–2026 papers, including 2026, need a plan.
Unlock from $6/mo1 “We eat more ice cream as the temperature rises.” What type of correlation is this? ................................................... [1]
3 Time Energy O What type of correlation does the scatter diagram show? .................................................[1]
13 The histogram shows information about the time, t minutes, spent in a shop by each of 80 people. 2 1 0 0 10 20 30 Time (minutes) t 40 50 60 70 Frequency density Complete the frequency table. Time (t minutes) t 0 5 1 G t 5 5 1 1 G t 15 30 1 G t 30 50 1 G t 50 70 1 G Number of people 6 27 10 [2]
18 The cumulative frequency diagram shows information about the time, m minutes, taken by 120 students to complete some homework. 120 100 80 60 40 20 0 0 10 20 30 Time (minutes) 40 50 60 m Cumulative frequency Use the cumulative frequency diagram to find an estimate of (a) the interquartile range, .......................................min [2] (b) the number of students who took more than 50 minutes to complete the homework. .............................................. [2]
18 120 students choose what they want to do when they leave school. Their choices are shown in the table. Choice Number of students University 57 Training 45 Work 18 Complete the pie chart to show this information. Label each sector clearly. [4]
21 The scatter diagram shows the value, in thousands of dollars, of eight houses in 1996 and the value of the same houses in 2016. 200 160 120 80 40 180 140 100 60 20 0 20 40 60 Value in 1996 ($ thousands) 80 100 10 30 50 70 90 Value in 2016 ($ thousands) (a) One of these eight houses had a value of $70 000 in 1996. Write down the value of this house in 2016. $ ................................................ [1] (b) The values of two more houses are shown in the table. Value in 1996 ($ thousands) 40 80 Value in 2016 ($ thousands) 80 150 On the scatter diagram, plot these values. [1] (c) On the scatter diagram, draw a line of best fit. [1] (d) Another house had a value of $50 000 in 1996. Find an estimate of the value of this house in 2016. $ ................................................ [1]
23 40 people were asked how many times they visited the cinema in one month. The table shows the results. Number of cinema visits 0 1 2 3 4 5 6 7 Frequency 5 5 6 6 7 3 6 2 (a) (i) Find the mode. .............................................. [1] (ii) Calculate the mean. .............................................. [3] (b) Omar wants to show the information from the table in a pie chart. Calculate the sector angle for the people who visited the cinema 5 times. .............................................. [2] Question 24 is printed on the next page.
24 The time, t minutes, 80 students each spend completing their homework is recorded. The cumulative frequency diagram shows the results. 0 10 0 10 20 30 40 Cumulative frequency 50 60 70 80 20 30 Time (minutes) 40 50 60 t Use the cumulative frequency diagram to find an estimate of (a) the median, ......................................... min [1] (b) the interquartile range, ......................................... min [2] (c) the number of students who spend more than 40 minutes completing their homework. ................................................ [2] Question 25 is printed on the next page.
2 The time taken for each of 120 students to complete a cooking challenge is shown in the table. Time (t minutes) 20 1 t G 25 25 1 t G 30 30 1 t G 35 35 1 t G 40 40 1 t G 45 Frequency 44 32 28 12 4 (a) (i) Write down the modal time interval. ................... 1 t G ................... [1] (ii) Write down the interval containing the median time. ................... 1 t G ................... [1] (iii) Calculate an estimate of the mean time. ......................................... min [4] (iv) A student is chosen at random. Find the probability that this student takes more than 40 minutes. ................................................. [1] (b) (i) Complete the cumulative frequency table. Time (t minutes) t G 20 t G 25 t G 30 t G 35 t G 40 t G 45 Cumulative frequency 0 44 [2] 5 (ii) On the grid, draw a cumulative frequency diagram to show this information. 20 0 10 20 30 40 50 60 70 80 90 100 110 120 t 25 30 35 Time (minutes) Cumulative frequency 40 45 [3] (iii) Find the median time. ......................................... min [1] (iv) Find the interquartile range. ......................................... min [2] (v) Find the number of students who took more than 37 minutes to complete the cooking challenge. ................................................. [2]
3 (a) The scatter diagram shows the physics mark and the chemistry mark for each of 12 students. 0 1 2 3 4 5 6 7 2 4 6 8 1 3 5 Physics mark Chemistry mark 7 10 0 9 (i) What type of correlation is shown in the scatter diagram? ................................................ [1] (ii) On the scatter diagram, draw a line of best fit. [1] (iii) Find an estimate of the chemistry mark for another student who has a physics mark of 4. ................................................ [1] (b) A teacher records the number of days each of the 24 students in her class are absent. The frequency table shows the results. Number of days 0 1 2 3 4 5 Frequency 10 8 3 2 0 1 Find the mode, the median and the mean. Mode = ............................................... Median = ............................................... Mean = ............................................... [5] 7 (c) Three sizes of eggs are sold in a shop. The table shows the number of eggs of each size sold in one day. Size Small Medium Large Mass (m grams) m 46 52 1 G m 52 62 1 G m 62 80 1 G Number of eggs sold 78 180 162 (i) Calculate an estimate of the mean mass. ............................................. g [4] (ii) On the grid, draw a histogram to show the information in the table. 0 2 4 6 8 10 Frequency density 12 14 16 18 20 50 40 60 Mass (grams) m 70 80 [4]
4 A school nurse records the height, h cm, of each of 180 children. The table shows the information. Height (h cm) h 60 70 1 G h 70 90 1 G h 90 100 1 G h 100 110 1 G h 110 115 1 G h 115 125 1 G Frequency 8 26 35 67 28 16 (a) Calculate an estimate of the mean. Give your answer correct to 1 decimal place. .......................................... cm [4] (b) In a histogram showing the information, the height of the bar for the interval h 60 70 1 G is 0.4 cm. Calculate the height of the bar for each of the following intervals. h 115 125 1 G .................................... cm h 110 115 1 G .................................... cm h 70 90 1 G ...................................... cm [3] (c) Complete the cumulative frequency table below. Height (h cm) h 70 G h 90 G h 100 G h 110 G h 115 G h 125 G Cumulative frequency 180 [2] (d) On the grid opposite, draw a cumulative frequency diagram. 7 60 0 20 40 60 80 100 Cumulative frequency Height (cm) 120 140 160 180 70 80 90 100 110 120 130 h [3] (e) Use your cumulative frequency diagram to find an estimate of (i) the interquartile range, .......................................... cm [2] (ii) the 70th percentile, .......................................... cm [2] (iii) the number of children with height greater than 106 cm. ................................................ [2]
5 (a) A factory recycles metal. The mass, x tonnes, of metal is measured each week. The table shows the results for 52 weeks. Mass (x tonnes) x 100 200 1 G x 200 250 1 G x 250 300 1 G x 300 500 1 G Frequency 8 20 12 12 (i) Calculate an estimate of the mean. ....................................... tonnes [4] (ii) 0 0 0.2 0.4 0.1 0.3 0.5 Frequency density Mass (tonnes) 100 200 300 400 500 x On the grid, draw a histogram to show the information in the table. [4] 11 (b) Another factory also recycles metal. The mass, x tonnes, of metal is measured each day for a number of days. The cumulative frequency diagram shows the results. 0 0 20 40 60 80 100 Cumulative frequency Mass (tonnes) 10 30 50 70 90 20 40 60 80 10 30 50 70 x (i) For how many days was the mass measured? .................................................. [1] (ii) Find an estimate of the median. ....................................... tonnes [1] (iii) Find an estimate of the upper quartile. ....................................... tonnes [1] (iv) Find an estimate of the interquartile range. ........................................tonnes [1] (v) Find an estimate of the number of days when the mass was greater than 20 tonnes. .................................................. [2]
7 The frequency table shows information about the time, m minutes, that each of 160 people spend in a library. Time (m minutes) m 0 10 1 G m 10 40 1 G m 40 60 1 G m 60 90 1 G m 90 100 1 G m 100 120 1 G Frequency 3 39 43 55 11 9 (a) (i) Find the probability that one of these people, chosen at random, spends more than 100 minutes in the library. ................................................ [1] (ii) Calculate an estimate of the mean time spent in the library. ......................................... min [4] (b) Complete the cumulative frequency table below. Time (m minutes) m 10 G m 40 G m 60 G m 90 G m 100 G m 120 G Cumulative frequency 3 42 [2] (c) On the grid opposite, draw the cumulative frequency diagram. 11 0 20 40 60 80 100 120 140 160 m 0 20 40 60 Time (minutes) Cumulative frequency 80 100 120 [3] (d) Use your cumulative frequency diagram to find (i) the median, ......................................... min [1] (ii) the interquartile range, ......................................... min [2] (iii) the 90th percentile, ......................................... min [2] (iv) the number of people who spend more than 30 minutes in the library. ................................................ [2]
9 (a) The table shows the amount of time, T minutes, 120 people each spend in a supermarket one Saturday. Time (T minutes) Number of people 10 1 T G 30 16 30 1 T G 40 18 40 1 T G 45 22 45 1 T G 50 40 50 1 T G 60 21 60 1 T G 70 3 (i) Use the mid-points of the intervals to calculate an estimate of the mean. ......................................... min [4] (ii) Complete this histogram to show the information in the table. 0 0 2 4 6 8 Frequency density Time (minutes) 10 20 30 40 50 60 70 T [4] 15 (b) This histogram shows the amount of time, T minutes, 120 people each spend in the supermarket one Wednesday. 0 0 2 4 6 8 Frequency density Time (minutes) 10 20 30 40 50 60 70 T Make a comment comparing the distributions of the times for the two days. .............................................................................................................................................................. .............................................................................................................................................................. [1]
4 Amber’s mean mark on five tests is 80. Her marks on four of these tests are 68, 81, 74 and 89. Work out her mark on the fifth test. ................................................... [2]
16 Six students revise for a test. The scatter diagram shows the time, in hours, each student spent revising and their mark in the test. 0 25 30 35 40 Mark 45 50 1 2 3 4 5 Time (hours) 6 7 8 9 10 (a) The data for two more students is shown in the table. Time (hours) 4.5 6.5 Mark 33 35 Plot these two points on the scatter diagram. [1] (b) What type of correlation is shown on the scatter diagram? .............................................. [1] (c) Draw a line of best fit on the scatter diagram. [1] (d) Another student spent 5.5 hours revising. Estimate a mark for this student. .............................................. [1]
21 The diagram shows the numbers of hummingbirds seen by Ali and Hussein in their gardens each day for 10 days. 1 0 1 2 3 4 5 6 7 8 9 2 3 4 5 Day Number of hummingbirds 6 7 8 9 10 Ali’s garden Hussein’s garden (a) Calculate the mean number of hummingbirds seen in Ali’s garden each day. ................................................. [3] (b) Work out the median number of hummingbirds seen in Hussein’s garden each day. ................................................. [2] (c) On one of these days there were 4 times as many hummingbirds seen in Hussein’s garden as in Ali’s garden. Which day was this? Day ................................................ [1]
22 Simon records the heights, h cm, of 200 sunflowers in his garden. The cumulative frequency diagram shows this information. 100 0 20 40 60 80 100 120 140 160 180 200 120 140 160 Height (cm) h Cumulative frequency 180 200 220 (a) Find the number of these sunflowers that have a height of more than 160 cm. ................................................... [2] (b) Sue records the heights, h cm, of 200 sunflowers in her garden. The cumulative frequency table shows this information. Height (h cm) Cumulative frequency h G 100 0 h G 110 20 h G 120 48 h G 130 100 h G 140 140 h G 150 172 h G 160 188 h G 170 200 On the grid above, draw another cumulative frequency diagram to show this information. [3] (c) Work out the difference between the median heights of Simon’s sunflowers and Sue’s sunflowers. ............................................. cm [2] Question 23 is printed on the next page.
2 The time taken for each of 90 cars to complete one lap of a race track is shown in the table. Time (t seconds) t 70 71 1 G t 7 72 1 1 G t 7 7 2 3 1 G t 7 7 3 4 1 G t 7 7 4 5 1 G Frequency 17 24 21 18 10 (a) Write down the modal time interval. ............... t 1 G ............. [1] (b) Calculate an estimate of the mean time. .............................................. s [4] (c) (i) Complete the cumulative frequency table. Time (t seconds) t 71 G t 72 G t 73 G t 74 G t 75 G Cumulative frequency 17 [2] 5 (ii) On the grid, draw a cumulative frequency diagram to show this information. 90 80 70 60 50 40 30 20 10 0 70 71 72 73 74 75 t Time (seconds) Cumulative frequency [3] (iii) Find the median time. .............................................. s [1] (iv) Find the inter-quartile range. .............................................. s [2] (d) One lap of the race track measures 3720 metres, correct to the nearest 10 metres. A car completed the lap in 75 seconds, correct to the nearest second. Calculate the upper bound for the average speed of this car. Give your answer in kilometres per hour. ....................................... km/h [4]
3 (a) 200 students estimate the capacity, x millilitres, of a cup. The results are shown in the frequency table. Capacity (x ml) x 0 100 1 G x 100 1 0 5 1 G x 150 00 2 1 G x 200 0 25 1 G x 250 00 4 1 G Frequency 20 55 66 35 24 (i) Calculate an estimate of the mean. ............................................. ml [4] (ii) Complete the histogram. 0.5 0 1 1.5 Frequency density 100 0 200 Capacity (ml) 300 400 x [4] 7 (b) The 200 students also estimate the mass, m grams, of a small rock. The results are shown in the cumulative frequency table. Mass (m grams) m 50 G m 0 10 G m 150 G m 0 20 G m 250 G Cumulative frequency 28 64 104 168 200 (i) On the grid, draw a cumulative frequency diagram. 50 0 100 150 200 Cumulative frequency 50 0 100 Mass (g) m 150 200 250 [3] (ii) Find (a) the 65th percentile, ............................................... g [1] (b) the number of students who estimated more than 75 g. ................................................... [2]