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Study Guide for Quantitative Analysis for Business
1. Qualitative vs. Quantitative Studies
● Quantitative Studies: Focus on numerical data. Examples include surveys with
numerical scales, statistical analyses, or experiments with measurable outcomes.
● Qualitative Studies: Focus on non-numerical data, such as opinions, interviews, or
open-ended survey responses.
● Tips: Identify the data type in a question; numbers = quant, opinions/words = qual.
2. Y-hat Equation
● Formula: Y=^a+b1x1+b2x2+b3x3Y\hat = a + b_1x_1 + b_2x_2 +
b_3x_3Y=^a+b1x1+b2x2+b3x3
1. a: Constant (always provided in the question).
2. b: Coefficients for the variables (x1,x2,x3x_1, x_2, x_3x1,x2,x3).
3. x: Values for the respective variables.
● Steps to Solve:
1. Plug in the values for aaa, bbb, and xxx.
2. Remember order of operations (multiplication before addition).
3. Simplify to get the result.
● Tip: Keep track of variable pairs bnb_nbn and xnx_nxn carefully to avoid errors.
3. Probabilities
● Key Concept:
○ For independent events: Add probabilities.
○ Example: If A=10%A = 10\%A=10% and D=25%D = 25\%D=25%, the probability
AAA and DDD happen = 10%+25%=35% 10\% + 25\% = 35\%10%+25%=35%.
○ Use decimal equivalents for percentages (e.g., 10%=0.1010\% = 0.1010%=0.10).
● Tip: If asking about the probability of a single event, just use the percentage directly.
4. Expected Values
● Formula: E(X)=∑(Probability×Value)E(X) = \sum (Probability \times
Value)E(X)=∑(Probability×Value)
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● Steps:
○ Multiply each percentage by its corresponding value.
○ Add the results for all items.
● Two Common Questions:
○ Comparison: Compare the expected values of different options and pick the
highest.
○ Single Expected Value: Calculate for one option using the formula.
● Tip: Focus on charts and extract relevant data carefully.
5. Decision Trees
● Concept: Another method to calculate expected values.
○ Multiply each outcome's probability by its value.
○ Add results to find the total expected value.
● Tip: Approach it the same way as expected values, but visualize the process
step-by-step on a decision tree.
6. Critical Path Method
● Critical Path:
○ Longest sequence of tasks that determines the total project duration.
● Duration Estimation:
○ Subtract the known durations from the total time to find the missing duration.
○ Example: Total = 202020, Known = 5+3+1+7=165 + 3 + 1 + 7 = 165+3+1+7=16.
Missing = 20−16=420 - 16 = 420−16=4.
● Tip: Ensure all tasks in the sequence are connected.
7. Linear Programming
1. Objective Function:
○ Maximize profit or minimize cost.
○ Use Z=aX1+bX2Z = aX_1 + bX_2Z=aX1+bX2, where a,ba, ba,b are coefficients.
2. Constraints:
○ Identify the limiting factor (time, materials, etc.).
○ Example: If time is finite, that's the constraint.
3. Feasible Region:
○ Solve inequalities to determine boundaries on a graph.
○ Use x=0x = 0x=0 or y=0y = 0y=0 to calculate intercepts.
4. Optimal Solution:
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Study Guide for Quantitative Analysis for Business
1. Qualitative vs. Quantitative Studies
● Quantitative Studies: Focus on numerical data. Examples include surveys with
numerical scales, statistical analyses, or experiments with measurable outcomes.
● Qualitative Studies: Focus on non-numerical data, such as opinions, interviews, or
open-ended survey responses.
● Tips: Identify the data type in a question; numbers = quant, opinions/words = qual.
2. Y-hat Equation
● Formula: Y=^a+b1x1+b2x2+b3x3Y\hat = a + b_1x_1 + b_2x_2 +
b_3x_3Y=^a+b1x1+b2x2+b3x3
1. a: Constant (always provided in the question).
2. b: Coefficients for the variables (x1,x2,x3x_1, x_2, x_3x1,x2,x3).
3. x: Values for the respective variables.
● Steps to Solve:
1. Plug in the values for aaa, bbb, and xxx.
2. Remember order of operations (multiplication before addition).
3. Simplify to get the result.
● Tip: Keep track of variable pairs bnb_nbn and xnx_nxn carefully to avoid errors.
3. Probabilities
● Key Concept:
○ For independent events: Add probabilities.
○ Example: If A=10%A = 10\%A=10% and D=25%D = 25\%D=25%, the probability
AAA and DDD happen = 10%+25%=35% 10\% + 25\% = 35\%10%+25%=35%.
○ Use decimal equivalents for percentages (e.g., 10%=0.1010\% = 0.1010%=0.10).
● Tip: If asking about the probability of a single event, just use the percentage directly.
4. Expected Values
● Formula: E(X)=∑(Probability×Value)E(X) = \sum (Probability \times
Value)E(X)=∑(Probability×Value)
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● Steps:
○ Multiply each percentage by its corresponding value.
○ Add the results for all items.
● Two Common Questions:
○ Comparison: Compare the expected values of different options and pick the
highest.
○ Single Expected Value: Calculate for one option using the formula.
● Tip: Focus on charts and extract relevant data carefully.
5. Decision Trees
● Concept: Another method to calculate expected values.
○ Multiply each outcome's probability by its value.
○ Add results to find the total expected value.
● Tip: Approach it the same way as expected values, but visualize the process
step-by-step on a decision tree.
6. Critical Path Method
● Critical Path:
○ Longest sequence of tasks that determines the total project duration.
● Duration Estimation:
○ Subtract the known durations from the total time to find the missing duration.
○ Example: Total = 202020, Known = 5+3+1+7=165 + 3 + 1 + 7 = 165+3+1+7=16.
Missing = 20−16=420 - 16 = 420−16=4.
● Tip: Ensure all tasks in the sequence are connected.
7. Linear Programming
1. Objective Function:
○ Maximize profit or minimize cost.
○ Use Z=aX1+bX2Z = aX_1 + bX_2Z=aX1+bX2, where a,ba, ba,b are coefficients.
2. Constraints:
○ Identify the limiting factor (time, materials, etc.).
○ Example: If time is finite, that's the constraint.
3. Feasible Region:
○ Solve inequalities to determine boundaries on a graph.
○ Use x=0x = 0x=0 or y=0y = 0y=0 to calculate intercepts.
4. Optimal Solution:
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