ANSWER KEYS - Teacher Use Only

Statistical Measures | Grade 6

Student Concept Worksheet Answers
1
Mean = 9, Median = 10, Mode = 10, Range = 6
Ordered: 6, 7, 10, 10, 12. Mean = 45/5 = 9. Median = 10 (middle). Mode = 10 (appears twice). Range = 12-6 = 6.
2
Mean = 35, Median = 35, Mode = 35, Range = 20
Ordered: 25, 30, 35, 35, 40, 45. Mean = 210/6 = 35. Median = (35+35)/2 = 35. Mode = 35. Range = 45-25 = 20.
3
Mean = 79.7, Median = 89
Ordered: 20, 85, 88, 90, 95, 100. Mean = 478/6 = 79.7. Median = (88+90)/2 = 89. The MEDIAN better represents typical value because 20 is an outlier pulling the mean down.
4
Mode
Mode shows the most common shoe size - what customers buy most often!
5
Median
The $1,200,000 house is an outlier. Median ($160,000) better represents typical prices than mean (which would be much higher).
Practice Worksheet Answers

Part A: Find All Measures

#Ordered DataMeanMedianModeRange
175, 82, 82, 86, 9083828215
28, 9, 10, 12, 12, 151111127
365, 68, 70, 72, 72, 75, 7871.4727213
414, 14, 14, 16, 18, 20, 2216.916148

Part B: Working with Outliers

5
Mean = $29.40, Median = $12, Outlier = $100
Median better represents typical allowance. The $100 outlier drastically increases the mean.
6
Mean = $469,000, Median = $215,000
Agent would prefer median because it's closer to what most buyers can afford. The $1.5M home skews the mean.
7
New Mean = $11.75, Change = $17.65
Without outlier: (10+12+15+10)/4 = 47/4 = $11.75. Original mean was $29.40, so change = 29.40 - 11.75 = $17.65

Part C: Choose Best Measure

8
Mode
Mode shows the most frequently purchased size.
9
Median
The score of 25 is an outlier that would pull the mean down.
10
Mean
When data is evenly distributed with no outliers, mean works well.

Part D: Word Problems

11
Current mean = 90, Needed score = 102
Current: (88+92+85+90+95)/5 = 450/5 = 90. For mean of 92 with 6 quizzes: 92 x 6 = 552 total needed. 552 - 450 = 102.
12
Mean = 4.5, Median = 4.5, Mode = 4 and 5 (bimodal)
Ordered: 2,3,4,4,5,5,6,7. Mean = 36/8 = 4.5. Median = (4+5)/2 = 4.5. Mode: both 4 and 5 appear twice.
13
B) There is an outlier pulling the mean up
Mean (15) > Median (12) > Mode (10) suggests there's a high outlier pulling the mean upward.

Challenge Questions:

#14: Many answers possible. Examples: 10, 10, 10, 10, 10 or 8, 10, 10, 10, 12 or 6, 10, 10, 10, 14

#15: Sixth number = 22. If mean = 20 and there are 6 numbers, total = 20 x 6 = 120. Sum of known five: 15+18+22+24+19 = 98. Missing: 120-98 = 22.

FAST Practice Quiz Answers
1
B) 4
Mean = (2+4+3+4+7)/5 = 20/5 = 4
2
B) 12
12 appears 3 times (most frequent). Mode = 12
3
A) Mean
The outlier (25) significantly pulls down the mean. Median and mode are barely affected.
4
Select: Mean is 20, Median is 20, No mode, Range is 10
Mean = 100/5 = 20 - TRUE
Median = 20 (middle of 5) - TRUE
No mode (all appear once) - TRUE
Range = 25-15 = 10 - TRUE
Mode is 20 - FALSE (there is no mode)
5
B) Median
The CEO salary ($2M) is an extreme outlier. Median would represent the typical employee salary much better than mean.
6
B) 11
Ordered: 6, 8, 10, 12, 12, 14. Middle two values: 10 and 12. Median = (10+12)/2 = 11
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for box plots, histograms, and comparing data sets.
4-5/6 Approaching Mastery Review specific concepts: ordering data, even-count median, or outlier effects.
2-3/6 Developing Use physical data cards. Practice with small data sets. Focus on one measure at a time.
0-1/6 Needs Intervention Start with mean only. Build understanding of average before adding other measures.
FAST Success Kit | Grade 6 | FL B.E.S.T. Standards: MA.6.DP.1.2, MA.6.DP.1.3 | Answer Key - Teacher Use Only