1. What is Normal Range Distribution?

The normal range distribution is a statistical method to determine the expected range of values in a normally distributed population. It's calculated as the mean plus or minus a multiple of the standard deviation.

2. How Does the Calculator Work?

The calculator uses the normal range formula:

Where:

• \( \mu \) — Mean of the distribution
• \( \sigma \) — Standard deviation
• \( k \) — Multiplier determining the range width

Explanation: For a normal distribution, about 68% of values fall within μ±1σ, 95% within μ±2σ, and 99.7% within μ±3σ.

3. Importance of Normal Range

Details: Normal ranges are crucial in medical testing, quality control, and statistical analysis to identify outliers and determine expected values.

4. Using the Calculator

Tips: Enter the mean, standard deviation, and desired multiplier (k). Common k values are 1 (68%), 2 (95%), and 3 (99.7%).

5. Frequently Asked Questions (FAQ)

Q1: What does k=2 represent?
A: k=2 gives approximately 95% coverage of values in a normal distribution (μ±2σ).

Q2: When is this range not appropriate?
A: When data is not normally distributed. Other methods like percentiles may be better for skewed distributions.

Q3: How is this used in medicine?
A: Lab tests often report reference ranges as mean ± 2SD, representing the 95% reference interval.

Q4: What if my SD is zero?
A: With SD=0, all values are identical to the mean, making the range just [μ, μ].

Q5: Can I use non-integer k values?
A: Yes, k can be any positive number. For example, k=1.96 gives exactly 95% coverage.