Summarizing Numeric Data with Measures of Center and Spread(TEKS.Math.6.12.C)
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Texas 6th Grade Math › Summarizing Numeric Data with Measures of Center and Spread(TEKS.Math.6.12.C)
A data set has these five-number summary values: min=12, Q1=18, median=24, Q3=31, max=40. What is the IQR (Q3 − Q1)?
13
11
19
28
Explanation
Compute the interquartile range: $IQR = Q_3 - Q_1 = 31 - 18 = 13$. The IQR of 13 shows the spread of the middle half of the data.
Ordered data (least to greatest): 3, 5, 5, 6, 7, 8, 9, 10, 12, 12, 14, 20. Which statement best compares the range and IQR for this set?
The range and IQR are equal.
The range is greater than the IQR.
The IQR is greater than the range.
The IQR is 17 and the range is 6.5.
Explanation
Range: $20 - 3 = 17$. For quartiles (12 values): $Q_1$ is the median of 3,5,5,6,7,8 → average of 5 and 6 is 5.5. $Q_3$ is the median of 9,10,12,12,14,20 → average of 12 and 12 is 12. So $IQR = Q_3 - Q_1 = 12 - 5.5 = 6.5$. Since 17 > 6.5, the range is greater than the IQR. This suggests the full spread is wider than the middle spread, possibly due to an outlier.
Ordered data (least to greatest): 12, 13, 15, 17, 18, 21, 22, 24, 30. What is the IQR (Q3 − Q1)?
9
7
8
12
Explanation
There are 9 values. The median is the 5th value (18). Lower half: 12, 13, 15, 17 → $Q_1$ is the average of 13 and 15, which is 14. Upper half: 21, 22, 24, 30 → $Q_3$ is the average of 22 and 24, which is 23. So $IQR = Q_3 - Q_1 = 23 - 14 = 9$. The middle half of the data varies by 9.