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Maths · Grade 6 · Set A
How Spread Out
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Remember: The range is the biggest less the smallest. The box holds the middle half, and the IQR is Q3 less Q1.

Range and quartiles

1
The range is the biggest number less the smallest. What is the range of this data? Answer:
2
The dot plots show two sets of data. Which set is more spread out?
The top setThe bottom set
3
These five numbers describe a data set. What is the interquartile range (IQR)? Answer:
4
Set Q has the larger range.
TrueFalse
5
Cut the list at the median. The median stays out of both halves. What is the third quartile, Q3, of this data? Answer:

Five numbers and spread around the mean

6
Which are the five numbers (smallest, Q1, median, Q3, biggest) for this data?
1, 2, 4, 5, 91, 2, 3, 7, 91, 2, 4, 7, 91, 2, 2, 7, 9
7
Join each word to what it tells you.
  1. 1range
  2. 2IQR
  3. 3median
  4. 4MAD
  • Athe average distance from the mean
  • Bthe middle number
  • Cbiggest less smallest
  • Dthird quartile less first quartile
8
The mean of this data is 4. Find how far each dot is from 4, then average those distances. What is the mean absolute deviation (MAD)? Answer:
9
Number the steps to find the IQR.
  • Put the data in order
  • Subtract: Q3 less Q1
  • Find Q1 and Q3, the middle of each half
  • Find the median

Stretch

10
Set X is on top and Set Y is below. Which set is more spread out? Write how you know.
11
A data set has range 14. Its smallest number is 6, as marked. What is its biggest number? Answer:
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Answer key · Set A
How Spread Out
16 The biggest is 8 and the smallest is 2. 8 − 2 = 6.
2The bottom set The bottom set runs from 1 to 10, a range of 9. The top set runs from 4 to 7, a range of 3.
311 The IQR is the third quartile less the first quartile: 25 − 14 = 11.
4False P has range 20 − 4 = 16. Q has range 15 − 9 = 6. P is the more spread out.
58 The median is 6. The upper half is 7, 8, 8, 10. Q3 is the middle of that half: between 8 and 8, so 8.
61, 2, 4, 7, 9 The median is 4. The lower half is 1, 2, 2, so Q1 = 2. The upper half is 5, 7, 9, so Q3 = 7.
71-C, 2-D, 3-B, 4-A The range uses the two ends. The IQR uses the middle half. The MAD uses every value.
82 The distances from 4 are 3, 1, 1, 1 and 4. They add to 10, and 10 ÷ 5 = 2.
91, 4, 3, 2
10Your own words: a grown-up reads it.
1120 Range = biggest − smallest, so biggest = 6 + 14 = 20.
Mark each answer, count the right ones and write the score on the sheet.