TI-84 Plus CE: 1-Var Stats Breakdown
The “1-Var Stats” function on the TI-84 Plus CE provides a summary of key statistics for a single variable data set. Here’s what each component of the output means:
1. x̄ (x-bar)
- Definition: The mean (average) of the data set.
- Calculation: Sum of all data points divided by the number of data points.
- Formula: xˉ=∑xnx̄ = \frac{\sum{x}}{n}xˉ=n∑x
2. Σx (Sum of x)
- Definition: The sum of all the data points.
- Calculation: Adds up every individual data point in the data set.
- Formula: Σx=x1+x2+…+xnΣx = x_1 + x_2 + … + x_nΣx=x1+x2+…+xn
3. Σx² (Sum of x squared)
- Definition: The sum of the squares of each data point.
- Calculation: Squares each data point and then sums them up.
- Formula: Σx2=x12+x22+…+xn2Σx² = x_1² + x_2² + … + x_n²Σx2=x12+x22+…+xn2
4. Sx (Sample standard deviation)
- Definition: The standard deviation of the data set when it represents a sample.
- Calculation: Measures the average distance of the data points from the mean.
- Formula: Sx=∑(xi−xˉ)2n−1Sx = \sqrt{\frac{\sum{(x_i - x̄)^2}}{n - 1}}Sx=n−1∑(xi−xˉ)2
5. σx (Population standard deviation)
- Definition: The standard deviation of the data set when it represents an entire population.
- Calculation: Measures the spread of the data points relative to the mean.
- Formula: σx=∑(xi−xˉ)2nσx = \sqrt{\frac{\sum{(x_i - x̄)^2}}{n}}σx=n∑(xi−xˉ)2
6. n
- Definition: The number of data points in the data set.
- Calculation: Simply the count of the total number of data entries.
7. minX (Minimum value)
- Definition: The smallest data point in the set.
- Significance: Indicates the lower bound of the data set.
8. Q1 (First Quartile)
- Definition: The median of the lower half of the data set.
- Significance: 25% of the data points are below this value.
9. Med (Median)
- Definition: The middle value of the data set when ordered from least to greatest.
- Significance: Splits the data set into two equal halves.
10. Q3 (Third Quartile)
- Definition: The median of the upper half of the data set.
- Significance: 75% of the data points are below this value.
11. maxX (Maximum value)
- Definition: The largest data point in the set.
- Significance: Indicates the upper bound of the data set.