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Maths · Grade 6 · Set B
How Spread Out? Set B
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Goal: 15 min
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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?
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)?
4
Set N has the larger IQR.
TrueFalse
5
Cut the list at the median. The median stays out of both halves. What is the first quartile, Q1, of this data?

Five numbers and spread around the mean

6
Which are the five numbers (smallest, Q1, median, Q3, biggest) for this data?
2, 3, 6, 8, 102, 3, 5, 6, 103, 3, 5, 8, 102, 3, 5, 8, 10
7
Join each word to what it tells you.
  1. 1first quartile, Q1
  2. 2third quartile, Q3
  3. 3range
  4. 4IQR
  • Ahow wide the middle half is
  • Bhow far it is from smallest to biggest
  • Cthe middle of the lower half
  • Dthe middle of the upper half
8
The mean of this data is 5. Find how far each dot is from 5, then average those distances. What is the mean absolute deviation (MAD)?
9
Number the steps to find the range of 9, 4, 12 and 7.
  • Subtract: 12 − 4
  • Find the biggest number, 12
  • Find the smallest number, 4
  • Write the range, 8

Stretch

10
A data set has range 15. Its smallest number is 8, as marked. What is its biggest number?
11
The IQR of a data set can be bigger than its range.
TrueFalse
12
Write one thing the dot plot tells you about how spread out the data is. Use the words smallest and biggest.
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Answer key · Set B
How Spread Out? Set B
18 The biggest is 11 and the smallest is 3. 11 − 3 = 8.
2The top set The top set runs from 1 to 14, a range of 13. The bottom set runs from 6 to 9, a range of 3.
37 The IQR is the third quartile less the first quartile: 15 − 8 = 7.
4True M has IQR 10 − 6 = 4. N has IQR 14 − 5 = 9. N is more spread out in the middle.
53 The median is 7. The lower half is 1, 2, 4, 5. Q1 is the middle of that half: between 2 and 4, so 3.
62, 3, 5, 8, 10 The median is 5. The lower half is 2, 3, 3, so Q1 = 3. The upper half is 6, 8, 10, so Q3 = 8.
71-C, 2-D, 3-B, 4-A Q1 and Q3 are middle numbers of the two halves. The range and the IQR are the distances.
81 The distances from 5 are 2, 0, 0 and 2. They add to 4, and 4 ÷ 4 = 1.
93, 1, 2, 4 Biggest less smallest.
1023 Range = biggest − smallest, so biggest = 8 + 15 = 23.
11False The IQR only covers the middle half, so it can never be longer than the whole spread from smallest to biggest.
12Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.