Students compute the range, interquartile range (IQR), and mean absolute deviation (MAD) to describe the spread of a data set. They interpret these measures in context and compare the variability of two data sets using the same measure.
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Grade 6 · Statistics and Data Analysis · question 1 of 3
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The IQR of 3, 4, 5, 6 is
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Range is the spread from smallest to largest.
Subtract the minimum from the maximum.
Read it: How spread out the data is
The data 4, 5, 8, 11, 12, 14 reaches from 4 to 14, so its range is 14 − 4 = 10. The middle of the lower half is 5 and the middle of the upper half is 12, so its IQR is 12 − 5 = 7.
Range: take the least value away from the greatest.
IQR: put the values in order and split them into a lower half and an upper half (with an odd count, the median is left out of both halves); find the middle of each, and take the lower middle away from the upper middle.
MAD: find the mean, then each value's distance from it, then the mean of those distances.
The range uses only the ends, so a single far-off value can stretch it.
The IQR is the spread of the middle half, so the far ends do not move it.
The MAD says how far the values sit from their mean, on average.
Range is greatest − least; the IQR is upper middle − lower middle; the MAD is the mean distance from the mean.
Calling the greatest value, 14, the range.
The range is the greatest take away the least: 14 − 4 = 10.
The range of 17, 5, 29, 13 is ___ — 24. The greatest is 29 and the least is 5: 29 − 5 = 24.
Range of 4, 7, 2, 9, 5
The range tells us how spread out the numbers in a data set are. Let's find the range of these long-jump distances.
Here are five jumps measured in feet: four, seven, two, nine, and five.
First, we put them in order from least to greatest.
The smallest value — the minimum — is two.
The largest value — the maximum — is nine.
The range equals the largest value minus the smallest value.
Grade 6 · Finding the range of a data set
Nine minus two is seven.
The range is seven feet — that's how spread out our jumps are. Nice work!
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MayaGrade 3 · Mathematics
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A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.
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Divide within 100
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MayaGrade 3 · Mathematics
Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.