Calculate Central Tendency - GMAT Quantitative Reasoning

1. Refer to the line graph. What is the range, in degrees Fahrenheit, of the daily high temperatures shown?
   Answer: 10 The highest value on the graph is $78^{\circ}F$ and the lowest is $68^{\circ}F$. Range $=78-68=10$. A) 8 and B) 9 result from mis-reading the extremes; D) 11 comes from subtracting 67 from 78, using an incorrect low point.
2. Based on the pie chart shown, what is the median number of clients per department?
   Answer: 16 Counts: Marketing 20, Finance 16, HR 12, Operations 24, IT 8. Ordered: 8,12,16,20,24 ⇒ median is 16. A) 12 and D) 20 are adjacent values, not the middle; C) 18 is an average of 16 and 20, not an actual count.
3. Based on the bar chart shown, what is the median number of books read by the seven students last month?
   Answer: 5 The bar heights are 3, 7, 4, 6, 2, 9, and 5. Ordered from least to greatest: 2, 3, 4, 5, 6, 7, 9. The middle (4th) value is 5, so the median is 5. A) 4 and C) 6 are the two values adjacent to the median but not the middle; D) 7 is larger than the median because it sits farther to the right in the ordered list.
4. A company calculates employee bonuses using a weighted average of three performance metrics: Quality (weight 40%), Efficiency (weight 35%), and Teamwork (weight 25%). If an employee's Quality score is 85, Efficiency score is 92, and the weighted average is 88, what is the Teamwork score?
   Answer: 87 Let T = Teamwork score. Weighted average formula: 0.40(85) + 0.35(92) + 0.25(T) = 88. Calculate: 0.40(85) = 34, 0.35(92) = 32.2. So: 34 + 32.2 + 0.25T = 88, which gives 66.2 + 0.25T = 88. Therefore: 0.25T = 88 - 66.2 = 21.8, so T = 21.8 ÷ 0.25 = 87.2 ≈ 87.
5. Use the dot plot below to determine the mean exam score.
   Answer: 78 Scores (each dot represents one student): 70,72,74,74,75,76,78,78,80,82,84. Sum $=858$; eleven scores ⇒ $858/11=78$. A) 76.4 omits 84; B) 77.2 mis-counts 74 twice; D) 78.8 double-counts 82.
6. In a data set of 20 values, the mean is 50 and the median is 48. If the 5 largest values are each decreased by 8, what is the new mean?
   Answer: 48.0 Original mean = 50, so total sum = 20 × 50 = 1000. When the 5 largest values are each decreased by 8, the total decrease in sum = 5 × 8 = 40. New sum = 1000 - 40 = 960. New mean = 960 ÷ 20 = 48.0. The median information is given as a distractor - it doesn't affect the calculation of the new mean when we know the original mean and the specific changes made.
7. Use the histogram shown to calculate the approximate mean age of the 40 participants.
   Answer: 29.9 Midpoints: 22,27,32,37. Weighted sum $6(22)+12(27)+15(32)+7(37)=1195$; $1195/40=29.875\approx29.9$. A) 28.7 uses wrong midpoint for 30–34; C) 30.6 mis-weights 35–39; D) 31.5 assumes each bin midpoint is 1 unit higher.
8. Refer to the tree diagram. What is the expected value of the investment's one-year return, in percent?
   Answer: 1.8 Weighted average: $0.60(5)+0.40(-3)=3-1.2=1.8\%$. A) 1.2 uses the negative branch only; C) 2.4 multiplies 0.60 by 4; D) 3.0 ignores the loss branch.

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