This tool will help you find accurate estimations for your project costs and timelines.

## How to Use the Calculator

To use this calculator, follow these steps:

- Enter the Sample Mean (x̄) in the first input field.
- Enter the Population Standard Deviation (σ) in the second input field.
- Enter the Sample Size (n) in the third input field.
- Click the “Calculate” button to get your result.

## How It Calculates the Results

This calculator uses the following formula to determine the confidence interval for the sample mean:

*Lower Bound:* x̄ – (1.96 * (σ / √n))

*Upper Bound:* x̄ + (1.96 * (σ / √n))

where:

- x̄ is the Sample Mean
- σ is the Population Standard Deviation
- n is the Sample Size

The Z-score used for a 95% confidence level is 1.96.

## Limitations

This calculator assumes a normal distribution and a known population standard deviation. It is most accurate for large sample sizes (n > 30). For smaller sample sizes or unknown population standard deviations, other techniques and considerations should be applied.

## Use Cases for This Calculator

### Calculate Mean:

To find the estimator for the mean, sum all values in the data set and then divide by the total number of values. This gives you the average value in the data, which serves as a good estimator for the mean.

### Estimate Median:

When determining the median estimator, sort the values from smallest to largest and find the middle value. If there is an even number of values, take the average of the two middle values to get the median.

### Compute Mode:

For estimating the mode, identify the value that appears most frequently in the dataset. This value is the mode estimator and represents the most common value in the data.

### Calculating Range:

To estimate the range, subtract the smallest value from the largest value in the dataset. The range provides an understanding of the spread of values in the data.

### Estimate Variance:

To find the estimator for variance, calculate the average of the squared differences between each value and the mean. This provides a measure of how spread out the values are from the mean.

### Calculate Standard Deviation:

To estimate standard deviation, take the square root of the variance. It gives you a clear understanding of the dispersion of data points around the mean.

### Estimate Skewness:

Skewness estimator helps you understand the symmetry of the data distribution. A positive skew indicates a tail on the right side, while a negative skew represents a tail on the left side of the distribution.

### Compute Kurtosis:

To estimate kurtosis, analyze the peakedness or flatness of the data distribution compared to a normal distribution. A higher kurtosis signifies a sharper peak in the data.

### Calculate Confidence Interval:

To estimate the confidence interval, use the mean and standard deviation of the data along with the desired confidence level. This range provides a likely range for where the true population parameter lies.

### Estimate Correlation Coefficient:

To find the estimator for correlation coefficient, analyze how two variables move in relation to each other. The coefficient ranges between -1 and 1, representing negative and positive correlations, respectively.