A smartphone’s final score is the average of its scores on all six aspects. Which smartphone has the highest final score?
Answer and solution
Correct answer: D
Solution
Answer: D — Delta
1. All phones have six equally weighted scores. Compare their sums; dividing each by 6 cannot change the ranking.
2. Totals: Alpha 345, Beta 328, Gamma 355, Delta 377, Epsilon 268.
3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data.
Detailed setup and verification:
Write each sum from the table: Alpha 70+80+85+35+25+50=345; Beta 50+60+55+45+60+58=328; Gamma 90+70+60+25+30+80=355; Delta 40+55+65+90+70+57=377; Epsilon 30+40+45+65+40+48=268.
Each mean divides its sum by the same positive 6. Therefore ranking the sums is exact and saves five divisions. Delta’s mean 62.833… exceeds Gamma 59.166… and Alpha 57.5. A phone leading on one axis need not have the highest overall average.
Verification: 3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
1. All phones have six equally weighted scores. Compare their sums; dividing each by 6 cannot change the ranking.
2. Totals: Alpha 345, Beta 328, Gamma 355, Delta 377, Epsilon 268.
3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data.
Detailed setup and verification:
Write each sum from the table: Alpha 70+80+85+35+25+50=345; Beta 50+60+55+45+60+58=328; Gamma 90+70+60+25+30+80=355; Delta 40+55+65+90+70+57=377; Epsilon 30+40+45+65+40+48=268.
Each mean divides its sum by the same positive 6. Therefore ranking the sums is exact and saves five divisions. Delta’s mean 62.833… exceeds Gamma 59.166… and Alpha 57.5. A phone leading on one axis need not have the highest overall average.
G Strategy shortcut
Method: Equal denominators: compare sums, not six separate decimal averages. Delta 377 wins.Verification: 3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data.
Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.
G Strategy: Method: Equal denominators: compare sums, not six separate decimal averages. Delta 377 wins. Verification: 3. The largest is Delta 377, with mean 377/6=62⅚. Answer D. The exact table and plotted values use the same data. Trap to avoid: Use the exact requested cohort, statistic or rank condition; the worked check above establishes the result.