Key Takeaways
- Mean (average) is calculated by dividing the sum of all values by the number of values
- Median is the middle value when data is arranged in order; for an even count, average the two middle values
- Mode is the most frequently occurring value in a data set; a data set can have no mode, one mode, or multiple modes
- Range is the difference between the highest and lowest values in a data set
- Bar graphs compare categories; line graphs show trends over time; pie charts show parts of a whole
- To solve a basic algebraic equation, isolate the variable by performing inverse operations on both sides
- Scientific notation expresses very large or very small numbers: a x 10^n (where 1 <= a < 10)
- Number line concepts: absolute value is the distance from zero, always positive or zero
Data Interpretation & Basic Algebra
Nurses regularly interpret data from patient charts, lab values, vital signs trends, and research articles. The HESI A2 tests your ability to calculate basic statistics, read graphs, and solve simple algebraic equations.
Measures of Central Tendency
Measures of central tendency describe the "center" or "typical value" of a data set:
Mean (Average)
Mean = Sum of all values / Number of values
Example: A patient's last 5 blood glucose readings are: 95, 110, 102, 88, 105
- Sum = 95 + 110 + 102 + 88 + 105 = 500
- Number of values = 5
- Mean = 500 / 5 = 100 mg/dL
When to use the mean: When data is evenly distributed without extreme outliers.
Median (Middle Value)
The median is the middle value when data is arranged in numerical order.
Steps:
- Arrange values from least to greatest
- If odd number of values → the middle value is the median
- If even number of values → average the two middle values
Example (odd): 88, 95, 102, 105, 110 → Median = 102 (3rd value)
Example (even): 88, 95, 102, 105, 108, 110
- Two middle values: 102 and 105
- Median = (102 + 105) / 2 = 103.5
When to use the median: When data has outliers or is skewed (the median is resistant to extreme values).
Mode (Most Frequent Value)
The mode is the value that appears most often.
Example: 98.6, 99.1, 98.6, 100.2, 98.6 → Mode = 98.6 (appears 3 times)
- A data set can have no mode (all values are different)
- A data set can have multiple modes (bimodal = 2 modes, multimodal = 3+)
Range
Range = Maximum value - Minimum value
Example: Blood pressures: 118, 124, 130, 142, 156
- Range = 156 - 118 = 38 mmHg
Reading Data Displays
| Type | Best For | How to Read |
|---|---|---|
| Bar graph | Comparing categories | Height/length of bars indicates value |
| Line graph | Showing trends over time | Slope indicates rate of change |
| Pie chart | Showing parts of a whole (percentages) | Larger slices = larger proportions |
| Table | Presenting exact numerical data | Read rows and columns carefully |
| Scatter plot | Showing relationships between two variables | Upward pattern = positive correlation |
HESI A2 Tip: When reading graphs, always check the axes labels, units, and scale before answering questions.
Basic Algebra
Solving One-Variable Equations
To solve for a variable, use inverse operations to isolate it:
| Operation | Inverse Operation |
|---|---|
| Addition (+) | Subtraction (-) |
| Subtraction (-) | Addition (+) |
| Multiplication (x) | Division (/) |
| Division (/) | Multiplication (x) |
Always perform the same operation on BOTH sides of the equation.
Example 1: x + 7 = 15
- Subtract 7 from both sides: x = 15 - 7 = 8
Example 2: 3x = 24
- Divide both sides by 3: x = 24 / 3 = 8
Example 3: 2x + 5 = 17
- Subtract 5: 2x = 12
- Divide by 2: x = 6
Example 4 (Nursing application): A patient needs 500 mL of fluid over 4 hours. The IV set delivers 15 drops/mL. What is the drip rate?
- Volume per hour = 500 / 4 = 125 mL/hr
- Drip rate = (125 mL x 15 drops/mL) / 60 min = 31.25 drops/min ≈ 31 drops/min
Scientific Notation
Scientific notation expresses numbers as: a x 10^n where 1 <= a < 10
| Standard Form | Scientific Notation |
|---|---|
| 45,000 | 4.5 x 10^4 |
| 300,000,000 | 3.0 x 10^8 |
| 0.005 | 5.0 x 10^-3 |
| 0.00000012 | 1.2 x 10^-7 |
Rules:
- Large numbers → positive exponent (move decimal left)
- Small numbers → negative exponent (move decimal right)
- The exponent tells you how many places the decimal moved
Nursing relevance: Lab values may use scientific notation, such as white blood cell counts (5.0 x 10^3 cells/mcL = 5,000 cells/mcL).
Absolute Value
Absolute value is the distance of a number from zero on the number line — always positive or zero.
| Number | Absolute Value |
|---|---|
| 5 | |
| -5 | |
| 0 | |
| -12.3 |
Integers and Number Properties
| Property | Definition | Example |
|---|---|---|
| Commutative | Order does not matter | a + b = b + a; a x b = b x a |
| Associative | Grouping does not matter | (a + b) + c = a + (b + c) |
| Distributive | Multiply across addition | a(b + c) = ab + ac |
| Identity | Adding 0 or multiplying by 1 gives the same number | a + 0 = a; a x 1 = a |
| Inverse | Number + its opposite = 0; number x its reciprocal = 1 | 5 + (-5) = 0; 5 x (1/5) = 1 |
A patient's temperature readings over 5 days are: 98.6, 99.2, 101.4, 98.8, 100.0. What is the mean temperature?
What is the median of the following data set: 72, 85, 68, 91, 76?
Solve for x: 3x - 9 = 18
The value that appears most frequently in a data set is called the _____.
Type your answer below
Match each measure of central tendency to its definition.
Match each item on the left with the correct item on the right
Express 0.00045 in scientific notation.
A data set contains the following values: 12, 15, 12, 18, 20, 15, 12. Which of the following are TRUE? (Select all that apply)
Select all that apply
A patient received 250 mL of IV fluid in the first hour and 175 mL in the second hour. What was the average hourly rate?