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TI-84 Statistics Tutorial

Master statistical analysis with your TI-84 calculator. Learn descriptive statistics, probability distributions, hypothesis testing, regression analysis, and data visualization techniques.

⏱️ 22 min read
πŸ“Š Intermediate Level
🎯 Statistics Guide

What You'll Learn

πŸ“ Entering and Managing Data

Statistical analysis begins with properly entering and organizing your data. The TI-84 uses lists to store data, and understanding how to work with lists is fundamental to all statistical operations.

Accessing the Statistics Editor

The STAT menu is your gateway to all statistical functions on the TI-84.

Opening the List Editor:

1
Press STAT: Access the statistics menu with the STAT key
2
Select Edit: Choose option 1:Edit to open the list editor
3
View Lists: You'll see columns L1, L2, L3, L4, L5, L6 for data entry

Entering Data into Lists

Data entry is straightforward, but there are techniques to make it more efficient.

Basic Data Entry:

1
Select List: Use arrow keys to move to the desired list (L1, L2, etc.)
2
Enter Values: Type each number and press ENTER to move to the next row
3
Navigate Data: Use arrow keys to move between cells and edit existing values
4
Delete Values: Press DEL to remove individual values or clear entire lists
Example Dataset - Test Scores:
L1: {85, 92, 78, 95, 88, 91, 82, 89, 94, 87}
Sample size: n = 10
Data represents student test scores out of 100

Managing Lists

Learn essential list operations for data management and cleanup.

Operation Method Key Sequence Purpose
Clear List Highlight list name, press CLEAR Arrow up to L1, CLEAR, ENTER Remove all data from list
Delete Entry Highlight entry, press DEL Navigate to value, DEL Remove single data point
Insert Entry Use 2ND DEL (INS) 2ND + DEL, enter value Add data point between others
Sort List STAT β†’ SortA( or SortD( STAT β†’ 2 or 3 Arrange data in order
Copy List L1 β†’ L2 on home screen 2ND + 1 β†’ 2ND + 2 Duplicate data to another list

Importing and Generating Data

Beyond manual entry, you can generate data patterns and sequences.

Generating Sequences:

1
Use seq( Function: 2ND + STAT β†’ OPS β†’ 5:seq(
2
Syntax: seq(expression, variable, start, end, step)
3
Example: seq(XΒ², X, 1, 10, 1) β†’ L1 creates squares 1, 4, 9, ..., 100

Data Entry Tips

β€’ Always check your data for typos before analysis
β€’ Use meaningful list names: Store data in named lists like SCORES or HEIGHTS
β€’ Keep paired data in adjacent lists (L1 and L2)
β€’ Sort data when calculating percentiles or creating ordered displays

πŸ“Š Descriptive Statistics

Descriptive statistics summarize and describe the main features of your dataset. The TI-84 can quickly calculate measures of central tendency, variability, and distribution shape.

One-Variable Statistics

Use 1-Var Stats to get a comprehensive summary of a single dataset.

Calculating Basic Statistics:

1
Access CALC Menu: Press STAT β†’ CALC β†’ 1:1-Var Stats
2
Specify List: Enter the list name (e.g., L1) or leave blank for L1 default
3
Execute: Press ENTER to calculate all statistics
4
Scroll Results: Use down arrow to see all calculated values
1-Var Stats Output Explained:
xΜ„ = 89.1 Sample Mean
Ξ£x = 891 Sum of Values
Ξ£xΒ² = 79767 Sum of Squares
Sx = 5.18 Sample Std Dev
Οƒx = 4.93 Population Std Dev
n = 10 Sample Size

Understanding the Statistics

Each statistic provides different insight into your data's characteristics.

Statistic Symbol Interpretation When to Use
Sample Mean xΜ„ Average value of dataset Measure of central tendency
Sample Standard Deviation Sx Variability around the mean When data is a sample
Population Standard Deviation Οƒx Variability for entire population When data is complete population
Minimum minX Smallest data value Range calculation, outlier detection
Maximum maxX Largest data value Range calculation, outlier detection
Median Med Middle value when sorted Skewed data, outliers present
Quartiles Q1, Q3 25th and 75th percentiles Box plots, IQR calculation

Two-Variable Statistics

When you have paired data, use 2-Var Stats to analyze relationships between variables.

Analyzing Paired Data:

1
Enter Paired Data: Put x-values in L1 and y-values in L2
2
Run 2-Var Stats: STAT β†’ CALC β†’ 2:2-Var Stats
3
Specify Lists: Enter L1, L2 (or your chosen lists)
4
Interpret Results: Review means, standard deviations, and correlation

Frequency Data

When data includes frequencies, use the frequency option for accurate calculations.

Example: Frequency Data
Values in L1: {70, 80, 90, 100}
Frequencies in L2: {3, 7, 12, 8}
Command: 1-Var Stats L1, L2
This represents: 3 scores of 70, 7 scores of 80, etc.

Sample vs Population

Use Sx (sample standard deviation) when your data represents a sample from a larger population. Use Οƒx (population standard deviation) only when you have data for the entire population. Most real-world scenarios use sample statistics.

πŸ“ˆ Data Visualization

Visual representations help you understand data patterns, outliers, and distributions. The TI-84 offers several plot types for different analytical purposes.

Setting Up Statistical Plots

Statistical plots are accessed through the STAT PLOT menu.

Accessing Plot Settings:

1
Open STAT PLOT: Press 2ND + Y= (STAT PLOT)
2
Select Plot: Choose Plot1, Plot2, or Plot3
3
Turn On Plot: Highlight "On" and press ENTER
4
Configure Settings: Choose plot type, lists, and display options

Types of Statistical Plots

Each plot type serves different analytical purposes.

Plot Type Icon Best Used For Data Requirements
Scatter Plot β‹…β‹…β‹… Relationships between two variables Paired data in two lists
Line Plot β‹…β€”β‹…β€”β‹… Trends over time Ordered paired data
Histogram β«΄β«΄β«΄ Distribution shape and frequency Single variable data
Box Plot β«·β«Έ Five-number summary, outliers Single variable data
Normal Prob Plot Normal curve Testing for normality Single variable data

Creating a Histogram

Histograms show the distribution shape and identify patterns in your data.

Histogram Setup:

1
Select Histogram: In STAT PLOT, choose the histogram icon
2
Choose Data List: Set Xlist to your data (e.g., L1)
3
Set Window: Press ZOOM β†’ 9:ZoomStat for automatic scaling
4
View Plot: Press GRAPH to display the histogram

Creating Box Plots

Box plots display the five-number summary and help identify outliers.

Box Plot Setup:

1
Choose Box Plot Type: Select regular box plot (β«·β«Έ) or modified box plot for outliers
2
Set Data Source: Choose your data list (L1, L2, etc.)
3
Configure Display: Use ZoomStat and Graph to view the plot
4
Read the Plot: Identify median, quartiles, and potential outliers

Scatter Plots and Correlation

Scatter plots reveal relationships between two variables.

Creating Scatter Plots:

1
Enter Paired Data: Put x-values in L1, y-values in L2
2
Set Plot Type: Choose scatter plot icon (first option)
3
Configure Lists: Set Xlist: L1, Ylist: L2
4
Choose Mark: Select point style (β–‘, +, β‹…)

Plot Interpretation Tips

β€’ Histograms: Look for shape (normal, skewed, bimodal)
β€’ Box plots: Check for symmetry and outliers (points beyond whiskers)
β€’ Scatter plots: Identify linear, nonlinear, or no relationship patterns
β€’ Use TRACE to read specific values from any plot

🎲 Probability Distributions

The TI-84 includes built-in functions for working with common probability distributions. These are essential for hypothesis testing and probability calculations.

Accessing Distribution Functions

Distribution functions are found in the DISTR menu.

Opening Distribution Menu:

1
Access DISTR: Press 2ND + VARS (DISTR)
2
Choose Function Type: Probability density (pdf), cumulative (cdf), or inverse functions
3
Select Distribution: Normal, binomial, t, chi-square, etc.

Normal Distribution

The normal distribution is fundamental to many statistical analyses.

Function Menu Option Syntax Purpose
normalcdf DISTR β†’ 2 normalcdf(lower, upper, ΞΌ, Οƒ) Find area under normal curve
invNorm DISTR β†’ 3 invNorm(area, ΞΌ, Οƒ) Find x-value for given probability
normalpdf DISTR β†’ 1 normalpdf(x, ΞΌ, Οƒ) Height of normal curve at x
ShadeNorm DISTR β†’ A ShadeNorm(lower, upper, ΞΌ, Οƒ) Visual area under curve
Normal Distribution Examples:
P(X < 85) with ΞΌ=80, Οƒ=5:
normalcdf(-∞, 85, 80, 5) = 0.8413

Find 95th percentile with ΞΌ=100, Οƒ=15:
invNorm(0.95, 100, 15) = 124.67

P(75 < X < 85) with ΞΌ=80, Οƒ=5:
normalcdf(75, 85, 80, 5) = 0.6827

Binomial Distribution

Use for discrete probability problems with fixed number of trials.

Binomial Calculations:

1
Exact Probability: binompdf(n, p, x) for P(X = x)
2
Cumulative Probability: binomcdf(n, p, x) for P(X ≀ x)
3
Example Parameters: n = trials, p = success probability, x = number of successes

Student's t-Distribution

Essential for small sample hypothesis testing and confidence intervals.

Function Syntax Purpose Common Use
tcdf tcdf(lower, upper, df) Area under t-curve P-values in t-tests
invT invT(area, df) Critical t-values Confidence intervals
tpdf tpdf(x, df) Height of t-curve Graphing t-distributions

Chi-Square Distribution

Used in goodness-of-fit tests and tests of independence.

Chi-Square Example:
Finding critical value for Ξ± = 0.05, df = 4:
invχ²(0.95, 4) = 9.488

P-value for χ² = 12.5, df = 4:
χ²cdf(12.5, ∞, 4) = 0.014

Distribution Parameter Order

Always check the parameter order for distribution functions! The TI-84 uses specific syntax: normalcdf(lower, upper, mean, std dev). Mixing up the order will give incorrect results.

πŸ“‰ Regression Analysis

Regression analysis helps you find mathematical relationships between variables and make predictions. The TI-84 supports multiple regression types for different data patterns.

Linear Regression

The most common regression type for finding straight-line relationships.

Performing Linear Regression:

1
Enter Data: Put x-values in L1, y-values in L2
2
Access Regression: STAT β†’ CALC β†’ 4:LinReg(ax+b)
3
Specify Lists: Enter L1, L2 (or your chosen lists)
4
Store Equation: Add Y1 to store regression line: LinReg(ax+b) L1, L2, Y1
Linear Regression Output:
a = 2.345 Slope
b = 15.67 Y-intercept
rΒ² = 0.847 Coefficient of Determination
r = 0.921 Correlation Coefficient

Interpreting Regression Results

Understanding what the statistics mean helps you evaluate the relationship quality.

Statistic Interpretation Good Values What It Tells You
Slope (a) Change in y per unit change in x Depends on context Direction and rate of relationship
Y-intercept (b) Value of y when x = 0 Meaningful in context Starting point of relationship
r (correlation) Strength of linear relationship |r| > 0.7 for strong How tightly points follow line
rΒ² (determination) Proportion of variation explained rΒ² > 0.64 for good fit Percentage of y explained by x

Other Regression Types

When data doesn't follow a straight line, try these alternatives.

Regression Type Menu Option Best For Equation Form
Quadratic CALC β†’ 5:QuadReg Parabolic patterns y = axΒ² + bx + c
Cubic CALC β†’ 6:CubicReg S-shaped curves y = axΒ³ + bxΒ² + cx + d
Exponential CALC β†’ A:ExpReg Exponential growth/decay y = abΛ£
Power CALC β†’ A:PwrReg Power relationships y = axᡇ
Logarithmic CALC β†’ 9:LnReg Logarithmic patterns y = a + b ln(x)

Making Predictions

Once you have a regression equation, use it to predict values.

Using Regression for Prediction:

1
Store Equation: Ensure regression equation is stored in Y1
2
Method 1 - TABLE: Use 2ND + GRAPH (TABLE) to see predictions
3
Method 2 - Substitute: On home screen, enter Y1(x-value) for specific prediction
4
Consider Validity: Only predict within reasonable range of data

Regression Best Practices

β€’ Always plot your data first to see the pattern
β€’ Check multiple regression types to find the best fit
β€’ Don't extrapolate far beyond your data range
β€’ Consider the context when interpreting rΒ² values
β€’ Look for outliers that might affect the regression

πŸ”¬ Hypothesis Testing

Hypothesis testing allows you to make statistical decisions about populations based on sample data. The TI-84 includes built-in tests for common scenarios.

Accessing Test Functions

Statistical tests are found in the STAT TESTS menu.

Opening Test Menu:

1
Access Tests: Press STAT β†’ TESTS
2
Choose Test Type: Z-tests, T-tests, or proportion tests
3
Input Method: Choose Data (from lists) or Stats (summary statistics)

One-Sample t-Test

Test whether a sample mean differs significantly from a hypothesized population mean.

Performing a t-Test:

1
Select Test: STAT β†’ TESTS β†’ 2:T-Test
2
Input Method: Choose Data (use list) or Stats (enter values manually)
3
Enter Values: ΞΌβ‚€ (null hypothesis), List/xΜ„, Sx, n
4
Choose Alternative: β‰ ΞΌβ‚€ (two-tailed), >ΞΌβ‚€ (right), <ΞΌβ‚€ (left)
5
Calculate: Highlight Calculate and press ENTER
t-Test Output Interpretation:
t = 2.34 Test Statistic
p = 0.043 P-value
df = 9 Degrees of Freedom
xΜ„ = 89.1 Sample Mean

Common Statistical Tests

The TI-84 supports a wide range of hypothesis tests for different scenarios.

Test Name Menu Option Use When Requirements
Z-Test TESTS β†’ 1 Testing mean, Οƒ known Normal population, Οƒ known
T-Test TESTS β†’ 2 Testing mean, Οƒ unknown Normal population, Οƒ unknown
2-SampZTest TESTS β†’ 3 Comparing two means Independent samples, Οƒ known
2-SampTTest TESTS β†’ 4 Comparing two means Independent samples, Οƒ unknown
1-PropZTest TESTS β†’ 5 Testing proportion Large sample, normal approximation
2-PropZTest TESTS β†’ 6 Comparing proportions Independent samples, large n

Confidence Intervals

Confidence intervals estimate the range of likely values for a population parameter.

Creating Confidence Intervals:

1
Access Intervals: STAT β†’ TESTS β†’ scroll to interval options (8, A, B, etc.)
2
Choose Type: ZInterval, TInterval, or proportion intervals
3
Set Confidence: Enter confidence level (0.95 for 95%, 0.99 for 99%)
4
Interpret Results: Note the interval bounds and margin of error

Interpreting Test Results

Understanding p-values and test statistics is crucial for drawing conclusions.

Decision Rules:
If p-value ≀ Ξ± (significance level):
β†’ Reject null hypothesis
β†’ Results are statistically significant

If p-value > Ξ±:
β†’ Fail to reject null hypothesis
β†’ Results are not statistically significant

Common Ξ± levels: 0.05, 0.01, 0.10

Statistical vs Practical Significance

A statistically significant result (low p-value) doesn't always mean the result is practically important. Always consider the magnitude of the effect and the real-world context when interpreting results.

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