Two friends, Ricky and Oliver, are picking berries. Each time they fill a carton its mass, in kg , is recorded. The masses are shown below: Ricky 0 . 145 0 . 182 0 . 135 0 . 132 0 . 112 0 . 155 0 . 189 0 . 132 0 . 145 0 . 201 0 . 139 Oliver 0 . 131 0 . 143 0 . 134 0 . 145 0 . 132 0 . 123 0 . 182 0 . 134 0 . 128 For each boy calculate the range of masses. (Take all answers correct up to hundredth place)

Given: Ricky 0 . 145 0 . 182 0 . 135 0 . 132 0 . 112 0 . 155 0 . 189 0 . 132 0 . 145 0 . 201 0 . 139 Oliver 0 . 131 0 . 143 0 . 134 0 . 145 0 . 132 0 . 123 0 . 182 0 . 134 0 . 128 We know that, Range = Largest value - smallest value For Ricky: The largest value = 0 . 201 The smallest value = 0 . 112 Range = 0 . 201 - 0 . 112 = 0 . 089 For Oliver: The largest value = 0 . 182 The smallest value = 0 . 123 Range = 0 . 182 - 0 . 123

The marks obtained by two classes in a Mathematics test are shown below. The marks are out of 20 . Class Archimedes 12 13 4 19 20 12 13 13 16 18 12 Class Bernoulli 13 6 9 15 20 20 13 15 17 19 3 Calculate the median score for each class.

Given: Class Archimedes 12 13 4 19 20 12 13 13 16 18 12 Class Bernoulli 13 6 9 15 20 20 13 15 17 19 3 Here, number of observations n = 11 We know that, when n is odd, Median = n + 1 2 t h observation For Archimedes: Ascending order of data, 4 , 12 , 12 , 12 , 13 , 13 , 13 , 16 , 18 , 19 , 20 ∴ Median = 11 + 1 2 = 12 2 = 6 t h observation Hence, Archimedes median is 6 t h observation, i.e., 13 . For Bernoulli: Ascending order of data, 3 , 6 , 9 , 13 , 13 , 15 , 15 , 17 , 19 , 20 , 20 ∴ Median = 11 + 1 2 = 12 2 = 6 t h observation Hence, Bernoulli's median is 6 t h observation, i.e., 15 .

The marks obtained by two classes in a Mathematics test are shown below. The marks are out of 20 . Class Archimedes 12 13 4 19 20 12 13 13 16 18 12 Class Bernoulli 13 6 9 15 20 20 13 15 17 19 3 Find the range of scores for each class?

Given: Class Archimedes 12 13 4 19 20 12 13 13 16 18 12 Class Bernoulli 13 6 9 15 20 20 13 15 17 19 3 We know that, Range = Largest value - smallest value For Archimedes: The largest value = 20 The smallest value = 4 Range = 20 - 4 = 16 Hence, Archimedes range is 16 . For Bernoulli: The largest value = 20 The smallest value = 3 Range = 20 - 3 = 17 Hence, Bernoulli's range is 17 .

Three shops sell light bulbs. A sample of 100 light bulbs is taken from each shop and the working life of each is measured in hours.The following table shows the mean time and range for each shop: Shop Mean (hours) Range (hours) Bright lights 136 18 Foot lights 145 36 Backlights 143 18 Which shop will you recommend to someone who is looking to buy a new light bulb and why?

Given: Shop Mean (hours) Range (hours) Bright lights 136 18 Foot lights 145 36 Backlights 143 18 To compare two or more sets of data, just comparing mean can sometimes be misleading. The larger the range, the more spread out the data is and the less consistent the values are with one another and vice versa. Foot light has the best mean but the range is large, whereas backlights and bright lights have the same range but backlights has a higher mean. Hence, I will recommend Backlights who is looking to buy a new light bulb.

Karen Morrison and Nick Hamshaw Solutions for Exercise 2: Exercise 12.2

Author:Karen Morrison & Nick Hamshaw

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 2: Exercise 12.2

Attempt the practice questions from Exercise 2: Exercise 12.2 with hints and solutions to strengthen your understanding. Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition solutions are prepared by Experienced Embibe Experts.

Questions from Karen Morrison and Nick Hamshaw Solutions for Exercise 2: Exercise 12.2 with Hints & Solutions

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 1

Two friends, Ricky and Oliver, are picking berries. Each time they fill a carton its mass, in $kg$ , is recorded. The masses are shown below:

Ricky	$0.145$	$0.182$	$0.135$	$0.132$	$0.112$	$0.155$	$0.189$	$0.132$	$0.145$	$0.201$	$0.139$
Oliver	$0.131$	$0.143$	$0.134$	$0.145$	$0.132$	$0.123$	$0.182$	$0.134$	$0.128$

For each boy calculate the range of masses. (Take all answers correct up to hundredth place)

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 1

Two friends, Ricky and Oliver, are picking berries. Each time they fill a carton its mass, in $kg$ , is recorded. The masses are shown below:

Ricky	$0.145$	$0.182$	$0.135$	$0.132$	$0.112$	$0.155$	$0.189$	$0.132$	$0.145$	$0.201$	$0.139$
Oliver	$0.131$	$0.143$	$0.134$	$0.145$	$0.132$	$0.123$	$0.182$	$0.134$	$0.128$

Which boy collected more berries per load?

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 1

Two friends, Ricky and Oliver, are picking berries. Each time they fill a carton its mass, in $kg$ , is recorded. The masses are shown below:

Ricky	$0.145$	$0.182$	$0.135$	$0.132$	$0.112$	$0.155$	$0.189$	$0.132$	$0.145$	$0.201$	$0.139$
Oliver	$0.131$	$0.143$	$0.134$	$0.145$	$0.132$	$0.123$	$0.182$	$0.134$	$0.128$

Which boy was more consistent while collecting the berries?

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 2

The marks obtained by two classes in a Mathematics test are shown below. The marks are out of $20$ .

Class Archimedes	$12$	$13$	$4$	$19$	$20$	$12$	$13$	$13$	$16$	$18$	$12$
Class Bernoulli	$13$	$6$	$9$	$15$	$20$	$20$	$13$	$15$	$17$	$19$	$3$

Calculate the median score for each class.

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 2

The marks obtained by two classes in a Mathematics test are shown below. The marks are out of $20$ .

Class Archimedes	$12$	$13$	$4$	$19$	$20$	$12$	$13$	$13$	$16$	$18$	$12$
Class Bernoulli	$13$	$6$	$9$	$15$	$20$	$20$	$13$	$15$	$17$	$19$	$3$

Find the range of scores for each class?

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 2

The marks obtained by two classes in a Mathematics test are shown below. The marks are out of $20$ .

Class Archimedes	$12$	$13$	$4$	$19$	$20$	$12$	$13$	$13$	$16$	$18$	$12$
Class Bernoulli	$13$	$6$	$9$	$15$	$20$	$20$	$13$	$15$	$17$	$19$	$3$

Which class did better in the test overall? (Archimedes/Bernoulli)

EASY

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 2

The marks obtained by two classes in a Mathematics test are shown below. The marks are out of $20$ .

Class Archimedes	$12$	$13$	$4$	$19$	$20$	$12$	$13$	$13$	$16$	$18$	$12$
Class Bernoulli	$13$	$6$	$9$	$15$	$20$	$20$	$13$	$15$	$17$	$19$	$3$

Which class was more consistent? (Archimedes/Bernoulli)

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 12 - Averages and Measures of Spread>Exercise 12.2>Q 3

Three shops sell light bulbs. A sample of $100$ light bulbs is taken from each shop and the working life of each is measured in hours.The following table shows the mean time and range for each shop:

Shop	Mean (hours)	Range (hours)
Bright lights	$136$	$18$
Foot lights	$145$	$36$
Backlights	$143$	$18$

Which shop will you recommend to someone who is looking to buy a new light bulb and why?

Karen Morrison and Nick Hamshaw Solutions for Exercise 2: Exercise 12.2

Karen Morrison Mathematics Solutions for Exercise - Karen Morrison and Nick Hamshaw Solutions for Exercise 2: Exercise 12.2

Questions from Karen Morrison and Nick Hamshaw Solutions for Exercise 2: Exercise 12.2 with Hints & Solutions

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