Statistics Banker

The ages, in years, of 9 children at a cricket academy in Sialkot are:12, 15, 11, 14, 12, 13, 16, 12, 12

1. (a) Write down the mode. [1]
2. (b) Find the median. [1]
3. (c) Find the range. [1]
4. (d) Calculate the mean. [2]

The rainfall, in mm, recorded in Lahore on 10 days in July was:0, 12.4, 3.6, 0, 25.0, 8.2, 0, 15.8, 4.4, 6.6

1. (a) Calculate the mean daily rainfall. [2]
2. (b) Find the median daily rainfall. [2]
3. (c) Find the range. [1]

At a motorway toll plaza, the number of people in each of 60 cars was counted.Number of people: 1, 2, 3, 4, 5Frequency: 23, 17, 9, 7, 4

1. (a) Write down the mode. [1]
2. (b) Find the median. [1]
3. (c) Calculate the mean number of people per car. [2]

A teacher asked her class how many books they read last month.Number of books: 0, 1, 2, 3Frequency: 3, x, 6, 4The mean number of books is 1.55.

1. (a) Show that 0.55x = 3.85. [2]
2. (b) Find x. [1]

The mean of five numbers is 8. Four of the numbers are 3, 7, 9 and 12.

1. (a) Find the fifth number. [2]
2. (b) A sixth number is added. The mean of the six numbers is now 9. Find the sixth number. [2]
3. (c) Find the range of the six numbers. [1]

The table shows the time, t minutes, that 60 commuters in Karachi took to travel to work.0 < t ≤ 10: 810 < t ≤ 20: 1520 < t ≤ 30: 2230 < t ≤ 40: 1040 < t ≤ 60: 5

1. (a) Calculate an estimate of the mean time. [4]
2. (b) Write down the modal class. [1]
3. (c) Write down the class that contains the median. [1]

A biology student measured the heights, in cm, of 11 bean seedlings:4.2, 5.8, 3.9, 6.1, 5.0, 4.7, 7.3, 5.5, 4.4, 6.6, 5.2

1. (a) Find the median. [1]
2. (b) Find the lower quartile and the upper quartile. [2]
3. (c) Find the interquartile range. [1]

The prices, in lakh rupees, of 7 houses sold in one street last year were:80, 95, 85, 90, 450, 88, 92

1. (a) Find the median price. [1]
2. (b) Find the mean price. [2]
3. (c) Explain why the median is a better average than the mean for these prices. [1]

Class A has 18 students and their mean mark in a test is 64.Class B has 22 students and their mean mark in the same test is 59.

1. (a) Calculate the mean mark of all 40 students. [2]
2. (b) Later it was found that one student in Class B scored 85, but the mark was recorded as 58. Calculate the correct mean mark of all 40 students. [2]

Four positive integers have a mode of 6, a median of 7 and a mean of 8.

1. (a) Find the four integers. [3]
2. (b) Find the range of the four integers. [1]

The mean of a list of n numbers is 12.

1. (a) The number 30 is added to the list and the mean becomes 13. Find n. [3]
2. (b) Two numbers, both equal to k, are then removed from the new list. The mean of the numbers left is 12. Find k. [2]

72 students were asked to choose their favourite sport.Cricket 30, Football 18, Hockey 12, Badminton 12

1. (a) Calculate the sector angle for each sport in a pie chart. [3]

The masses, in kg, of 15 parcels at a courier office are:23, 31, 18, 27, 35, 42, 29, 31, 24, 19, 38, 31, 26, 40, 33

1. (a) Draw an ordered stem-and-leaf diagram for these masses. Include a key. [3]
2. (b) Find the median. [1]
3. (c) Find the range. [1]

A pictogram shows the number of cups of chai sold at a school canteen. One symbol represents 8 cups.Monday: 3½ symbolsTuesday: 2¼ symbols

1. (a) How many cups were sold on Monday? [1]
2. (b) How many cups were sold on Tuesday? [1]
3. (c) On Wednesday 22 cups were sold. How many symbols should be drawn for Wednesday? [1]

A pie chart shows the main cooking fuel used by 240 households in a village.

1. (a) The sector for LPG has an angle of 66°. How many households use LPG? [2]
2. (b) 30 households use wood. Calculate the sector angle for wood. [2]

The two-way table shows how 120 students travel to school.Bus: boys 24, girls ?, total 45Car: boys ?, girls 18, total 31Walk: boys ?, girls 21, total ?Total: boys 60, girls ?, total 120

1. (a) Complete the table. [3]
2. (b) What percentage of the students walk to school? Give your answer correct to 1 decimal place. [2]

Two groups of athletes ran 100 m. Their times, in seconds, are shown as stem-and-leaf diagrams.Group A: 12 | 8 13 | 2 7 9 14 | 1 4 15 | 0Group B: 12 | 5 9 13 | 0 4 14 | 7 15 | 8 16 | 2Key: 13 | 2 means 13.2 seconds

1. (a) Find the median time for each group. [2]
2. (b) Find the range for each group. [2]
3. (c) Make two comparisons between the times of the two groups. [2]

In a pie chart showing people's favourite colours, the sector angles are:red 3x°, blue (2x + 10)°, green 90°, yellow (x + 20)°.

1. (a) Find x. [2]
2. (b) 18 people chose yellow. How many people were asked altogether? [2]

Two pie charts show what happened to a town's waste.In 2020 the town produced 480 tonnes of waste and the sector for 'recycled' was 75°.In 2025 the town produced 600 tonnes of waste and the sector for 'recycled' was 96°.

1. (a) Find the mass of waste recycled in each year. [2]
2. (b) Calculate the percentage increase in the mass recycled from 2020 to 2025. [2]

Fifteen students recorded the number of text messages they sent in one day:12, 30, 7, 15, 21, 3, 18, 24, 10, 36, 8, 27, 15, 13, 20

1. (a) Find the median. [1]
2. (b) Find the lower quartile and the upper quartile. [2]
3. (c) Write down the five values needed to draw a box plot. [1]

The masses of 200 apples were recorded. The cumulative frequency curve passes through these points (mass in g, cumulative frequency):(100, 0), (120, 14), (130, 38), (134, 50), (140, 72), (148, 100), (155, 124), (160, 150), (170, 182), (180, 196), (190, 200)

1. (a) Find the median mass. [1]
2. (b) Find the interquartile range. [2]
3. (c) Find the number of apples with a mass of more than 170 g. [1]

Box plots show the journey times, in minutes, of students at two schools.School P: minimum 12, lower quartile 18, median 23, upper quartile 30, maximum 41School Q: minimum 10, lower quartile 21, median 25, upper quartile 28, maximum 35

1. (a) Find the range and the interquartile range of the journey times for School P. [2]
2. (b) Make two comparisons between the journey times for the two schools. [2]

The heights, h cm, of 80 plants are shown.0 < h ≤ 10: 610 < h ≤ 20: 1420 < h ≤ 30: 2830 < h ≤ 40: 2240 < h ≤ 60: 10

1. (a) Write down the cumulative frequencies. [2]
2. (b) Use linear interpolation within the class to estimate the median height. [2]
3. (c) Estimate the number of plants taller than 35 cm. [2]

Write down the type of correlation you would expect between each pair of quantities.

1. (a) the temperature on a summer day and the number of ice creams sold at a beach in Karachi [1]
2. (b) the age of a car and its value [1]
3. (c) a student's shoe size and their mark in a history test [1]

The table shows the number of hours, h, eight students revised and their test scores, s (out of 100).h: 2, 5, 1, 8, 4, 6, 3, 7s: 41, 58, 35, 75, 52, 63, 46, 70

1. (a) Calculate the mean number of hours and the mean score. [2]
2. (b) Describe the correlation. [1]
3. (c) A line of best fit passes through the point of means and through (0, 28). Use the line to estimate the score of a student who revised for 5.5 hours. [2]
4. (d) Explain why it would not be sensible to use the line to estimate the score of a student who revised for 15 hours. [1]

On the same afternoon, a geography group recorded the height above sea level, h metres, and the temperature, T °C, at seven places in northern Pakistan.h: 500, 1200, 2000, 2600, 3100, 3800, 4500T: 31, 27, 21, 18, 14, 10, 5

1. (a) Describe the correlation and what it shows. [2]
2. (b) The equation of the line of best fit is T = 34.4 − 0.0065h. Use it to estimate the temperature at a place 3400 m above sea level. [2]
3. (c) Explain why the line should not be used to estimate the temperature at the summit of a mountain 8000 m high. [1]

The table shows the engine size, in litres, and the fuel economy, in km per litre, of seven cars.Engine size: 1.0, 1.3, 1.6, 1.8, 2.0, 2.4, 3.0Fuel economy: 18, 16.5, 15, 9, 13, 11.5, 8

1. (a) One car does not fit the trend. Write down its engine size. [1]
2. (b) The line of best fit passes through (1.0, 18) and (3.0, 8). Find its gradient and explain what it means in this context. [3]
3. (c) Use the line to estimate the fuel economy of a car with a 2.2-litre engine. [1]

The ages, a years, of 150 visitors to the Lahore Museum one morning are shown.0 < a ≤ 10: 2010 < a ≤ 25: 4525 < a ≤ 40: 3640 < a ≤ 60: 3460 < a ≤ 90: 15

1. (a) Calculate the frequency density for each class, to draw a histogram. [3]
2. (b) Which class has the tallest bar? [1]

A histogram shows the time, t minutes, that students took to finish a puzzle. The heights of the bars (frequency densities) are:0 < t ≤ 5: 2.45 < t ≤ 10: 410 < t ≤ 20: 3.220 < t ≤ 40: 0.8

1. (a) Find the frequency for each class and the total number of students. [3]
2. (b) Estimate the number of students who took more than 15 minutes. [2]

The masses, m grams, of fish caught by a boat at Gwadar are summarised.0 < m ≤ 100: 12100 < m ≤ 150: ?150 < m ≤ 200: 30200 < m ≤ 300: ?300 < m ≤ 500: 8On the histogram, the bar for 0 < m ≤ 100 has frequency density 0.12, the bar for 100 < m ≤ 150 has frequency density 0.46 and the bar for 200 < m ≤ 300 has frequency density 0.21.

1. (a) Find the two missing frequencies. [2]
2. (b) Find the frequency densities for the classes 150 < m ≤ 200 and 300 < m ≤ 500. [2]
3. (c) Calculate an estimate of the mean mass. Give your answer correct to 1 decimal place. [4]