IGCSE Maths Statistics topical questions

A data set is 2, 7, 9, 4, 7, 7.

1. (a)State the mode.[1]
2. (b)Find the median.[2]
3. (c)Find the range.[1]

80 pupils record how they travel to school. 30 walk (18 boys and 12 girls), 28 come by car (15 boys), and 22 take the bus (10 girls).

1. (a)Complete the two-way table.[2]
2. (b)How many girls come by bus?[1]
3. (c)What fraction of the girls walk to school?[1]

Maya has taken 4 tests with a mean score of 68.

1. (a)Find the total of her four scores.[2]
2. (b)She wants a mean of 70 after a fifth test. What score does she need?[3]

Goals scored in 20 matches: 0 goals ×7, 1 goal ×5, 2 goals ×4, 3 goals ×2, 4 goals ×2.

1. (a)Calculate the mean number of goals.[3]
2. (b)Find the median number of goals.[2]

90 people name their favourite fruit: apple 36, banana 27, orange 18, grape 9.

1. (a)Show that apple represents 144° on a pie chart.[2]
2. (b)Calculate the other three angles.[2]
3. (c)How many degrees represent one person?[1]

A scatter diagram of hours of practice x against competition score y follows the line of best fit y = 0.5x + 2, with data collected for 0 ⩽ x ⩽ 15.

1. (a)Describe the correlation shown.[1]
2. (b)Estimate the score for 10 hours of practice.[2]
3. (c)Explain why the line should not be used to estimate the score for 40 hours.[2]

Test scores are 42, 51, 47, 55, 61, 43, 52, 68, 45 and 57.

1. (a)Draw an ordered stem-and-leaf diagram using tens as stems.[3]
2. (b)Find the median score.[2]

A pie chart shows journeys to work for 240 people: bus 150°, car 120°, walking 60° and cycling 30°.

1. (a)Find the number of journeys by bus.[2]
2. (b)Find the number of journeys by cycle.[1]
3. (c)What fraction of the journeys was made on foot? Give your answer in its simplest form.[2]
4. (d)Verify that the four category counts match the 240 total.[1]

Weights (w kg) of 20 parcels: 10 ⩽ w < 20 (5 parcels), 20 ⩽ w < 30 (12), 30 ⩽ w < 40 (3). (Extended)

1. (a)Calculate an estimate of the mean weight.[3]
2. (b)State the modal class.[1]
3. (c)Explain why the mean is an estimate.[1]

The times of 60 swimmers are grouped, and their cumulative frequencies are: ⩽20 min (4), ⩽24 min (10), ⩽28 min (22), ⩽32 min (40), ⩽36 min (54), ⩽40 min (60). A smooth curve is drawn through these points. (Extended)

1. (a)Use the curve to estimate the median time.[2]
2. (b)Estimate the lower and upper quartiles and hence the interquartile range.[3]
3. (c)Estimate how many swimmers took longer than 32 minutes.[1]

A histogram has classes 0 < w ⩽ 10 with frequency density 1.2, 10 < w ⩽ 15 with frequency density 4, and 15 < w ⩽ 30 with frequency density 1.6. (Extended)

1. (a)Find the frequency of the 10 < w ⩽ 15 class.[2]
2. (b)Find the total frequency.[2]
3. (c)What fraction of the data lies in the 15 < w ⩽ 30 class? Give your answer as a fraction in its lowest terms.[2]

Salaries (s £1000s) of 80 employees: 10 ⩽ s < 20 (14 staff), 20 ⩽ s < 30 (26), 30 ⩽ s < 40 (22), 40 ⩽ s < 50 (12), 50 ⩽ s < 60 (6). (Extended)

1. (a)Calculate an estimate of the mean salary.[4]
2. (b)Write down the class interval that contains the median salary.[1]
3. (c)Explain why the estimate of the mean may not equal the true mean.[2]

Call lengths (t minutes) of 80 calls give cumulative frequencies: ⩽20 (10), ⩽30 (26), ⩽40 (50), ⩽50 (68), ⩽60 (80). (Extended)

1. (a)Estimate the median call length from the curve.[2]
2. (b)Estimate the interquartile range.[3]
3. (c)Estimate how many calls lasted longer than 45 minutes.[2]

Two shops record daily takings over 10 days. Shop A: mean 412, IQR 38. Shop B: mean 405, IQR 96. One day in shop B took 1200. (Extended)

1. (a)Which shop has the higher average takings?[1]
2. (b)Which shop’s takings are more consistent? Give a reason.[2]
3. (c)Give one reason the IQR is preferred to the range when comparing spread.[2]
4. (d)Describe the effect of the 1200 day on shop B’s mean, range and IQR.[2]