Testinar Grade 6 math

Measures of Spread

Students will build Grade 6 mastery of measures of spread using models, equations, and test-style reasoning.

CH05-04 Statistics and Probability

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

What is the range of the data set \(15, 22, 9, 30, 18\)?
1. \(21\)
2. \(18\)
3. \(9\)
4. \(30\)
The data set \(8, 12, 5, 19, 11, 6, 20\) is displayed on a number line. What is the range?
1. \(5\)
2. \(12\)
3. \(15\)
4. \(20\)
For the data set \(3, 7, 4, 9, 2, 8, 5\), arrange in order: \(2, 3, 4, 5, 7, 8, 9\). The median is \(5\) and the upper quartile is \(8\). What is the lower quartile?
1. \(2\)
2. \(5\)
3. \(4\)
4. \(3\)
A data set has minimum value \(12\), Q1 \(= 18\), median \(= 25\), Q3 \(= 32\), and maximum value \(40\). What is the interquartile range?
1. \(7\)
2. \(14\)
3. \(28\)
4. \(32\)
Using the ordered data \(10, 14, 16, 22, 24, 26, 30, 35\), find Q1 and Q3, then compute the interquartile range.
1. \(6\)
2. \(12\)
3. \(13\)
4. \(25\)
A box plot of test scores shows Q1 \(= 72\), median \(= 80\), and Q3 \(= 88\). Which value represents the interquartile range?
1. \(8\)
2. \(16\)
3. \(20\)
4. \(88\)
Two data sets have the same mean of \(50\) but different spreads. Set A has a range of \(12\) and Set B has a range of \(30\). What does this tell you?
1. Set A has more variation than Set B.
2. The range cannot be compared between sets.
3. Both sets have identical variation.
4. Set B has more variation than Set A.
For the data set \(2, 4, 6, 8\), the mean is \(5\). Calculate the MAD.
1. \(1\)
2. \(2\)
3. \(3\)
4. \(5\)

Teacher and parent reference

Answer key and explanations

A. \(21\)
Range \(=\) maximum \(-\) minimum \(=30-9=21\).
C. \(15\)
Maximum is \(20\), minimum is \(5\). Range \(= 20 - 5 = 15\).
D. \(3\)
The lower half of the ordered data is \(2, 3, 4\). The median of the lower half (lower quartile, Q1) is \(3\).
B. \(14\)
IQR \(= Q3 - Q1 = 32 - 18 = 14\). This measures the spread of the middle \(50\%\) of the data.
C. \(13\)
Split the ordered data into two halves. The lower half is \(10,14,16,22\), so \(Q1=\frac{14+16}{2}=15\). The upper half is \(24,26,30,35\), so \(Q3=\frac{26+30}{2}=28\). The IQR is \(28-15=13\).
B. \(16\)
IQR \(= Q3 - Q1 = 88 - 72 = 16\). The IQR tells us the spread of the middle half of the scores.
D. Set B has more variation than Set A.
A larger range indicates greater spread. Set B's range of \(30\) is larger than Set A's range of \(12\), so Set B has more variability.
B. \(2\)
Distances: \(|2-5|=3\), \(|4-5|=1\), \(|6-5|=1\), \(|8-5|=3\). MAD \(= \frac{3+1+1+3}{4} = \frac{8}{4} = 2\).