KS3 data handling quantitative data - continuous and discrete

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Maths Quiz - Level 5-6 Data Handling - Quantitative Data (Questions)

In KS3 Maths, dealing with data means encountering two main types - quantitative and qualitative. Qualitative data includes non-numerical things like colours, gender, or favourite films. On the other hand, quantitative data involves numbers, like the count of people with red hair, the number of males or females in a school, or how many liked the latest Star Wars film.

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Now, within quantitative data, there are two types: countable (discrete) and measurable (continuous). Discrete data always gives whole numbers (think how many kids like apples; you can't have half a person!). Measurable data might give fractions (like measuring a building's height, say 11.37 metres). Spot the difference? Recognising and handling these types of quantitative data is essential in KS3 Maths.

Try this quiz learn the difference between discrete and continuous quantitative data. Good luck!

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If data can only take certain numerical values it is called discrete. Which of these types of data is discrete?

[ ]	The colour of an apple
[ ]	The number of pips in an apple
[ ]	The volume (in cm³) of an apple
[ ]	The weight (in g) of an apple

If data can be measured against a scale it is called continuous. Which of these types of data is continuous?

[ ]	The beds in wards of a town's hospital
[ ]	The heights of buildings in a town
[ ]	The names of roads in a town
[ ]	The number of pupils in a town's schools

Adults responding to a survey are asked to choose their age group from these: 18-25, 25-40, 40-60, over 60. What is wrong with this choice?

[ ]	No ages below 18
[ ]	Age group intervals are all different
[ ]	Intervals overlap
[ ]	'Over 60' is too vague

Which of these can be read from a grouped frequency table of children's heights (h cm) recorded in 10cm intervals?

[ ]	Heights of individual children
[ ]	The height range
[ ]	The median height
[ ]	The modal height interval

The frequency recorded in the interval 130 < h ≤ 140 is 5. This means that five children are .......

[ ]	at least 130cm tall
[ ]	less than 140cm tall
[ ]	135cm tall
[ ]	over 130cm and up to 140cm tall

Which of these intervals would include a height of 130cm?

[ ]	125 ≤ h &LT; 130
[ ]	130 &LT; h ≤ 140
[ ]	120 &LT; h ≤ 130
[ ]	h >130

The contents of seed packets are recorded to the nearest 10. A pack with 43 seeds is recorded as having .......

[ ]	30 seeds
[ ]	35 seeds
[ ]	40 seeds
[ ]	45 seeds

A packet of 50 seeds (to the nearest 10) will contain at least .......

[ ]	44 seeds
[ ]	45 seeds
[ ]	54 seeds
[ ]	55 seeds

The contents of 20 packets of seeds (to the nearest 10) are: 5 x 30, 9 x 40, 5 x 50, 1 x 60. What is the best estimate for the total number of seeds in these packs?

[ ]	630
[ ]	750
[ ]	820
[ ]	940

10.

The contents of 20 packets of seeds (to the nearest 10) are: 5 x 30, 9 x 40, 5 x 50, 1 x 60. What is the best estimate for the mean (average) contents of these seed packets?

[ ]	41
[ ]	42
[ ]	43
[ ]	44

Maths Quiz - Level 5-6 Data Handling - Quantitative Data (Answers)

If data can only take certain numerical values it is called discrete. Which of these types of data is discrete?

[ ]	The colour of an apple
[x]	The number of pips in an apple
[ ]	The volume (in cm³) of an apple
[ ]	The weight (in g) of an apple

An apple only has half a pip if it's been cut in half

If data can be measured against a scale it is called continuous. Which of these types of data is continuous?

[ ]	The beds in wards of a town's hospital
[x]	The heights of buildings in a town
[ ]	The names of roads in a town
[ ]	The number of pupils in a town's schools

Height can be measured against a continuous scale

Adults responding to a survey are asked to choose their age group from these: 18-25, 25-40, 40-60, over 60. What is wrong with this choice?

[ ]	No ages below 18
[ ]	Age group intervals are all different
[x]	Intervals overlap
[ ]	'Over 60' is too vague

Adults are 18 or over. Someone aged 25 or 40 wouldn't know which box to tick

Which of these can be read from a grouped frequency table of children's heights (h cm) recorded in 10cm intervals?

[ ]	Heights of individual children
[ ]	The height range
[ ]	The median height
[x]	The modal height interval

As the heights are grouped into 10cm intervals we do not know any of the heights exactly and therefore can't find out the range, median or any individual hights

The frequency recorded in the interval 130 < h ≤ 140 is 5. This means that five children are .......

[ ]	at least 130cm tall
[ ]	less than 140cm tall
[ ]	135cm tall
[x]	over 130cm and up to 140cm tall

< means that they are more than 130cm tall and ≤ means they are less than or equal to 140cm tall

Which of these intervals would include a height of 130cm?

[ ]	125 ≤ h &LT; 130
[ ]	130 &LT; h ≤ 140
[x]	120 &LT; h ≤ 130
[ ]	h >130

The sign ≤ means 'less than or equal to'

The contents of seed packets are recorded to the nearest 10. A pack with 43 seeds is recorded as having .......

[ ]	30 seeds
[ ]	35 seeds
[x]	40 seeds
[ ]	45 seeds

This is simple rounding down

A packet of 50 seeds (to the nearest 10) will contain at least .......

[ ]	44 seeds
[x]	45 seeds
[ ]	54 seeds
[ ]	55 seeds

45 is the lowest number that can be rounded up to 50

The contents of 20 packets of seeds (to the nearest 10) are: 5 x 30, 9 x 40, 5 x 50, 1 x 60. What is the best estimate for the total number of seeds in these packs?

[ ]	630
[ ]	750
[x]	820
[ ]	940

(5 x 30) + (9 x 40) + (5 x 50) + (1 x 60)

10.

The contents of 20 packets of seeds (to the nearest 10) are: 5 x 30, 9 x 40, 5 x 50, 1 x 60. What is the best estimate for the mean (average) contents of these seed packets?

[x]	41
[ ]	42
[ ]	43
[ ]	44

820 / 20 = 41