6th Grade Statistical Variability Chapter Questions
1. How does data help us make decisions?
2. How can data be used to make predictions?
Chapter Problems
Measures of Center
Classwork
Find the mean, median, and mode for the following data sets.
1) 5.8, 2.9, 6.7, 1.6, 2.9, 4.7
2) 17, 16, 18, 15, 2
3) 7, 3, 10, 5, 5, 6, 6
4) 149, 124, 116, 118, 109, 108, 114, 124, 109
5) 22.3, 22.4, 23.3, 24.5, 22.5
6) 18.99, 17.99, 19.99, 17.99, 17.99, 17.00, 10.99
7) 750, 850, 700, 650, 450
8) 48, 50, 60, 51, 56, 51, 54, 61, 52, 52
Homework
Find the mean, median, and mode for the following data sets.
9) 92, 86, 90, 72, 95, 100, 90, 50
10) 0, 0.3, 0, 0.1, 0, 0.5, 0.2, 0.3
11) 25, 85, 40, 45, 95, 75, 55
12) 118, 116, 130, 106, 116, 146, 143, 129, 121
13) 0.95, 1.09, 0.99, 1.25, 0.99, 1.99
14) 456, 398, 655, 508, 1,186, 625
15) 58, 51, 33, 33, 6, 25, 25
16) 14, 15, 14, 16, 17, 14, 13, 15, 17, 14
Central Tendency Application Problems
Classwork
17) Jordan scored 85, 90, 72, 88, and 92 on his last 5 science tests. What score does he need in
order to have a mean score of 85 in his class?
18) Mary and her family share a family data plan for their cell phones. This month her mom used
450, her father used 380, and her little sister used 230 minutes. They want their average
number of minutes to be 375 minutes. How many minutes should Mary use?
19) Thomas’s bowling average needs to be at least a 250 in order to make his school’s team. In his
last 4 games, he bowled a 243, 271, 218, and 252. What does he need to bowl in his last game
in order to make the team?
20) Find the mean, median, and mode of the data set: 59, 85, 61, 88, 95, 75, 55. Identify the values
that remain the same if “75” is added to the set.
21) Find the mean, median and mode of the data set: 19, 18, 21, 18, 18, 14. Identify the values
that remain the same if “18” is added to the set.
22) Find the mean, median and mode of the data set: 3, 8, 3, 5, 3, 6, 4, 1, 3. Identify the values that
remain the same if “2” is added to the set.
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Homework
23) Tonya bought gifts for her family that cost $25, $14, $33, and $19. She has to buy one more
gift and wants her mean cost to be $25. What should she spend on the last gift?
24) Brianna scored 93, 87, 98, 81, 79, and 95 on her last 6 social studies tests. What score does she
need in order to have a mean score of 90?
25) Jake is training for the 200-meter dash event at the preliminary competition. During his last 4
attempts at practice, he ran it in 22.3 s, 22.4 s, 23.3 s, and 24.5 s. He needs a mean time of 23
seconds in order to qualify for finals. What time does he need for his final attempt?
26) Find the mean, median, and mode of the data set: 51, 43, 37, 39, 6, 30, 25. Identify the values
that remain the same if “33” is added to the set.
27) Find the mean, median, and mode of the data set: 2, 3, 1, 3, 1, 6, 4, 4, 3. Identify the values
that remain the same if “5” is added to the set.
28) Find the mean, median, and mode of the data set: 20, 21, 21, 18, 22, 20, 25. Identify the values
that remain the same if “23” is added to the set.
Measures of Variation – Minimum/Maximum, Range
Classwork
Find the minimum, maximum, and range of each of the following data sets.
29) 30, 31, 28, 18, 30, 4, 1
30) 20, 21, 21, 18, 22, 20, 25
31) 204, 138, 177, 218, 195, 249, 155, 108
32) 72, 95, 80, 80, 87, 80, 81, 62, 83, 87, 92, 64, 86
33) 0.95, 1.09, 0.99, 1.25, 0.99, 1.99
34) 456, 398, 655, 508, 1,186, 625
Homework
Find the minimum, maximum, and range of each of the following data sets.
35) 17, 16, 18, 15, 2
36) 5.8, 2.9, 6.5, 1.6, 2.9, 4.7
37) 48, 50, 60, 51, 56, 51, 54, 61, 52, 52
38) 149, 124, 116, 118, 109, 108, 114, 124, 109
39) 61, 52, 40, 54, 70, 34, 66, 38, 67, 75, 56, 71
40) 10.5, 11.6, 9.8, 7.3, 5.6, 12.1, 8.2, 5.7
Measures of Variation – Quartiles
Classwork
Find the lower quartile (Q1), median (Q2), upper quartile (Q3) and the interquartile range (IQR) of each
of the following data sets.
41) 9, 17, 11, 16, 18, 15, 2
42) 7, 3, 10, 5, 5, 6, 6, 8, 4
43) 220, 340, 130, 180, 230, 340, 100
44) 48, 50, 60, 51, 56, 51, 54, 61, 52, 52
45) 149, 124, 116, 118, 109, 108, 114, 124, 109
46) 14, 3, 7, 22, 18, 25, 12, 38
47) 15, 10, 12, 16, 18, 5, 3, 46, 35, 21, 26
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Homework
Find the lower quartile (Q1), median (Q2), upper quartile (Q3) and the interquartile range (IQR) of each
of the following data sets.
48) 52, 41, 33, 39, 6, 30, 25
49) 25, 85, 35, 45, 95, 75, 55
50) 20, 10, 50, 60, 40, 30, 90, 70
51) 118, 112, 130, 106, 116, 146, 143, 129, 134
52) 150, 132, 116, 118, 109, 108, 114, 124
53) 64, 53, 51, 90, 76, 68, 92, 81, 62, 98
54) 9, 10, 12, 9, 18, 12, 13, 10, 5, 8, 16, 11
Measures of Variation – Outliers
Classwork
55) Which of the following data sets have outlier(s)? Explain how you found your answer.
a. 1, 5, 7, 9, 10, 11, 15
b. 25, 39, 49, 53, 56, 60
c. 18, 19, 20, 24, 30, 60
d. 70, 74, 76, 79, 82, 83
e. 6, 27, 30, 33, 39, 41, 52
Homework
56) Which of the following sets of data have outlier(s)? Explain how you found your answer.
a. 90, 92, 93, 94, 97, 100
b. 48, 50, 51, 51, 54, 56, 65
c. 4, 20, 27, 28, 33, 34, 37
d. 64, 67, 68, 69, 73, 75, 79
e. 18, 33, 38, 39, 42, 43, 46
Measures of Variation – Mean Absolute Deviation
Classwork
Find the mean absolute deviation for each of the following data sets. Round to the nearest hundredth as
necessary.
57) 5, 8, 2, 1, 4, 6, 9
58) 111, 125, 101, 94, 136
59) 7, 10, 7, 10, 6, 7, 2
60) 33, 14, 17, 21, 8, 30, 29, 15
61) 20, 10, 50, 60, 40, 30, 90, 70
62) 150, 131, 116, 118, 109, 108, 114, 124
63) 54, 50, 62, 51, 63, 70, 58, 60, 60, 70
64) 19, 21, 24, 18, 20, 20, 19, 17, 20, 23
Homework
65) 15, 10, 24, 25, 27, 40
66) 11, 10, 12, 9, 18, 12
67) 4, 8, 46, 32, 25, 21, 11
68) 5, 6, 11, 14, 12, 8, 16, 18
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69)
70)
71)
72)
220, 340, 120, 180, 230, 340, 100, 70
25, 85, 35, 45, 95, 75, 55, 35
13, 22, 27, 16, 36, 7, 27, 33, 36, 36
6, 7, 2, 9, 6, 0, 20, 10, 16, 18
Chapter Review Multiple Choice
Choose the correct answer for each question. No partial credit will be given.
1. Consider the data set: 78, 81, 100, 69, 97, 81, 86
Select the measure of central tendency that has the greatest value.
a. Median
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b. Mean
c. Mode
2. Consider the data set: 55, 79, 90, 81, 90, 70, 65
Select the statement that is false
a. Mode: 90; Median: 79
b. Median: 79; Range: 45
c. Mean: 75.7; Range: 35
d. Mean: 75.7; Median: 79
3. Sam has the following test grades: 85, 98, 79
What must Sam score on the one remaining test if he wants his test average to be an 88?
a. 87
b. 88
c. 89
d. 90
4. Find the lower quartile (Q1), median (Q2), and upper quartile (Q3) for the given data set. 82, 94,
100, 86, 68, 89, 78, 84
a. Q1: 78; Q2: 84; Q3: 91.5
b. Q1: 82; Q2: 85; Q3: 91.5
c. Q1: 80; Q2: 85; Q3: 94
d. Q1: 80; Q2: 85; Q3: 91.5
5. Identify the data set that contains at least one outlier.
a. 5, 20, 22, 30, 18, 14
b. 34, 48, 65, 72, 81, 67, 37
c. 45, 31, 32, 51, 55, 53, 48
d. 2, 5, 8, 10, 1, 12, 9, 13, 13,
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6. Find the mean absolute deviation, rounded to the nearest hundredth, for the given data set.
20, 45, 52, 60, 19, 34, 42
a.33.86
b. 12.45
c. 87.14
d. 12.48
7. Mary paired one word to each measure of central tendency. Identify the most accurate pairing.
a. mean – average; mode – middle; median – often
b. mean – often; mode – middle; median – average
c. mean – average; mode – often; median – middle
d. mean – middle; mode – often; median - average
Short Constructed Response – Write the correct answer for each question. No partial credit will be
given.
8. Determine the mean, median and mode for the data set. Round your answers to the nearest
hundredth if necessary.
86, 88, 89, 78, 56, 80, 65
9. Using the test scores from question #14, determine the score that Sal must obtain on his next
test to have a 78 average?
Extended Constructed Response
10. Find the measures of variability for the data set below. Round to the nearest hundredth if
necessary.
131, 145, 67, 89, 127, 156, 189
a. Find the range.
b. Find the interquartile range.
c. Find the mean absolute deviation.
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Answer Key
1) Mean: 4.1
Median: 3.8
Mode: 2.9
2) Mean: 13.6
Median: 16
Mode: No mode
3) Mean: 6
Median: 6
Mode: 5 and 6
4) Mean: 119
Median: 116
Mode: 109 and 124
5) Mean: 23
Median: 22.5
Mode: No mode
6) Mean: 17.28
Median: 17.99
Mode: 17.99
7) Mean: 680
Median: 700
Mode: No mode
8) Mean: 53.5
Median: 52
Mode: 51 and 52
9) Mean: 84.375
Median: 90
Mode: 90
10) Mean: 0.175
Median: 0.15
Mode: 0
11) Mean: 60
Median: 55
Mode: No mode
12) Mean: 125
Median: 121
Mode: 116
13) Mean: 1.21
Median: 1.04
Mode: 0.99
14) Mean: 638
Median: 566.5
Mode: No mode
15) Mean: 33
Median: 33
Mode: 25 and 33
16) Mean: 14.9
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17)
18)
19)
20)
21)
22)
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24)
25)
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
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37)
38)
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Median: 14.5, Mode: 14
83
440 minutes
266
Median
Mean, Median, and Mode
Median and Mode
$34
97
22.5 s
Mean =33
Median = 37
Mode = no mode
Add 33 to numbers:
Mean = 33, the same
Median = 35, different
Mode = no mode, the same
Median and Mode
Median & Mode
Minimum: 1
Maximum: 31, Range: 30
Minimum: 18
Maximum: 25, Range: 7
Minimum: 108
Maximum: 249, Range: 141
Minimum: 62
Maximum: 95, Range: 33
Minimum: 0.95
Maximum: 1.99, Range: 1.04
Minimum: 398
Maximum: 1,186, Range: 788
Minimum: 2
Maximum: 18, Range: 16
Minimum: 1.6
Maximum: 6.5, Range: 4.9
Minimum: 48
Maximum: 61, Range: 13
Minimum: 108
Maximum: 149, Range: 41
Minimum: 34
Maximum: 75, Range: 41
Minimum: 5.6
Maximum: 12.1, Range: 6.5
Q1: 9
Q2: 15
Q3: 17
IQR: 8
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42) Q1: 4.5
Q2: 6
Q3: 7.5
IQR: 3
43) Q1: 130
Q2: 220
Q3: 340
IQR: 210
44) Q1: 51
Q2: 52
Q3: 56
IQR: 5
45) Q1: 109
Q2: 116
Q3: 124
IQR: 15
46) Q1: 9.5
Q2: 16
Q3: 23.5
IQR: 14
47) Q1: 10
Q2: 16
Q3: 26
IQR: 16
48) Q1: 25
Q2: 33
Q3: 41
IQR: 16
49) Q1: 35
Q2: 55
Q3: 85
IQR: 50
50) Q1: 25
Q2: 45
Q3: 65
IQR: 40
51) Q1: 114
Q2: 129
Q3: 138.5
IQR: 24.5
52) Q1: 111.5
Q2: 117
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Q3: 128
IQR: 16.5
53) Q1: 62
Q2: 72
Q3: 90
IQR: 28
54) Q1: 9
Q2: 10.5
Q3: 12.5
IQR: 3.5
55) C, E
56) B, E
57) 2.29
58) 13.68
59) 1.71
60) 7.38
61) 21.25
62) 10.31
63) 5.24
64) 1.54
65) 7.33
66) 2
67) 11.43
68) 3.75
69) 70
70) 21.56
71) 8.64
72) 5.28
Unit Review
1. B
2. B
3. D
4. D
5. A
6. B
7. C
8. MEAN: 77.43, MEDIAN: 80
MODE: NO MODE
9. 82
10. A. Range=122
B. Interquartile Range=67
C. Mean Absolute Deviation=29.8
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