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Maths · Grade 6 · Set C
How Spread Out? Set C
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C
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Goal: 15 min
Score/ 11
Remember: The range is the biggest less the smallest. The box holds the middle half, and the IQR is Q3 less Q1.

Bigger sets of data

1
Each dot is one value. What is the range of this data?
2
Which are the five numbers (smallest, Q1, median, Q3, biggest) for this data?
2, 5, 9, 12, 152, 4, 8, 12, 152, 5, 8, 12, 152, 5, 8, 11, 15
3
What is the interquartile range (IQR) of the same data?
4
There are 8 values, so cut the list into two halves of 4. Q1 and Q3 are the middles of the halves. What is the IQR?
5
Look at the two teams' five numbers. Which sentence is true?
Blues have the larger range and the larger IQRReds have the larger range and the larger IQRReds have the larger range, but Blues have the larger IQRBlues have the larger range, but Reds have the larger IQR

Spread around the mean

6
The mean of this data is 7. Find how far each dot is from 7, then average those distances. What is the MAD?
7
The mean of this data is 2.5. What is the MAD?
8
Here are the five numbers of a data set. What is its IQR?
9
When every number in a data set is the same, the range and the IQR are both 0.
TrueFalse
10
Number the steps to find the first quartile, Q1.
  • Put the data in order
  • Look at the lower half
  • Find the middle of the lower half: that is Q1
  • Find the median and cut the list into two halves

Stretch

11
Join each description to its name.
  1. 1third quartile less first quartile
  2. 2biggest less smallest
  3. 3the middle number
  4. 4the average distance from the mean
  • Arange
  • BMAD
  • CIQR
  • Dmedian
12
Class X is the top plot and class Y is the bottom plot. Which class's scores are more alike? Write how you know.
Scan the code at the top to mark this sheet on screenTake a photo of your answers or type them. It is marked for you automatically, and your score is kept.
Answer key · Set C
How Spread Out? Set C
113 The biggest is 15 and the smallest is 2. 15 − 2 = 13.
22, 5, 8, 12, 15 The median is 8, the 6th of 11. The lower half is 2, 3, 5, 5, 6, so Q1 = 5. The upper half is 9, 11, 12, 12, 15, so Q3 = 12.
37 The IQR is Q3 less Q1: 12 − 5 = 7.
46.5 The lower half is 1, 2, 4, 4, so Q1 = 3. The upper half is 7, 9, 10, 13, so Q3 = 9.5. 9.5 − 3 = 6.5.
5Reds have the larger range, but Blues have the larger IQR Reds: range 30 − 4 = 26, IQR 16 − 11 = 5. Blues: range 19 − 8 = 11, IQR 17 − 10 = 7. Reds have the larger range and Blues the larger IQR.
63 The distances from 7 are 5, 3, 1, 1, 3 and 5. They add to 18, and 18 ÷ 6 = 3.
71.25 The distances from 2.5 are 1.5, 0.5, 0.5 and 2.5. They add to 5, and 5 ÷ 4 = 1.25.
811 The IQR is the third quartile less the first quartile: 31 − 20 = 11.
9True Nothing is spread out. The biggest less the smallest is 0, and Q3 less Q1 is 0.
101, 3, 4, 2 Order, halve, then find the middle of the lower half.
111-C, 2-A, 3-D, 4-B The range uses the two ends, the IQR the middle half, and the MAD every value.
12Your own words: a grown-up reads it.
Mark each answer, count the right ones and write the score on the sheet.