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# Range

Updated on April 25, 2024
Article byPrakhar Gajendrakar
Edited byShreya Bansal
Reviewed byDheeraj Vaidya, CFA, FRM

## Range Definition

Range in trading refers to the difference between the highest and lowest prices of a stock within a given period, defining a bracket of data representation, particularly in statistics. This serves as a measure of price volatility, which correlates with risk, making it a significant risk indicator.

For eg:
Source: Range (wallstreetmojo.com)

It is assessed within a specific time frame, whether short-term or long-term. A wider gap signifies higher volatility, while a narrower gap indicates lower stock price volatility, a preference among investors. Moreover, statisticians often employ predefined ranges for descriptive purposes in their research when dealing with extensive data sets.

### Key Takeaways

• Range definition in trading is the difference between a dataset or stock’s highest and lowest price points determining volatility.
• It is plotted on price charts for any given single time frame as high or low price points on a candlestick or bar.
• Investors can indulge in range-bound trading, given that stock remains at a particular price over time.
• In statistics, it is used with other factors such as mean, median, mode, and standard deviation and is used in business studies and research.

### Range Explained

Range in statistics is used to determine the difference between the highest and lowest value of any given dataset. The two values depict a bracket for the data, elaborating the fluctuation of data points between them and indicating the variability. In any quantitative dataset, there are different values taken as individual data points or observations; in these values, there is always a highest value and, conversely, a lowest value; when the latter is subtracted from the former, the outcome is accounted as the range of the underlying data.

It is commonly deduced in financial markets to showcase the difference between the highest and lowest price of a stock for any given trading period. The range-bound trading is managed by prices staying in the defined range over time. It has a support price and a resistance price in between which the prices typically fluctuate.

Any stock’s trading value depends on the sector in which it operates, including several other market factors that influence it directly or indirectly. For example, treasure bonds and government securities have a smaller trading value compared to convertible securities. Likewise, commodities and equities have a larger value than fixed-income instruments. At the same time, many forms of data are necessarily informed in the form of a range, considering the fluctuations.

### Formula

The formula for the range is as follows:

Range = highest observation – lowest observation

1. Highest Observation: This refers to the highest value or data point in the dataset.
2. Lowest Observation: This refers to the lowest value or data point in the dataset.

To find the range, one subtracts the lowest observation from the highest observation. This calculation gives the spread or difference between the highest and lowest values in the dataset.

### Examples

Below are two examples to understand the concept in a better way.

#### Example #1

Suppose an investor is looking at the price chart of a particular stock for the last four minutes, and in that time, the stock price fluctuates nine times, forming a series 45.09, 45.45, 46.17, 47.07, 44.10, 48.06, 49.69, 50.49, 52.29

Now, if the investor wants to calculate the range of the underlying stock’s price, he can employ the formula –

Range = highest value – lowest value

• Range = 52.29 – 44.10
• Range = 8.19

Therefore, the value for the underlying stock in those four-minute time spans is calculated to be 8.19 by the investor. Based on this value, the investor can measure the risk of investing in the stock and make further decisions.

#### Example #2

In May 2023, Bitcoin experienced a period of significant stagnation in the crypto market, characterized by a tight trading range that lasted for several months. Many traders believe that tiger prices are the outcome of competing influences and volatility explosion. Bitcoin has stayed at its price despite the country’s debt ceiling stability.

The range of the difference between the high and the low price for seven days was 3.4%. It is the narrowest the cryptocurrency has gone in the past three years. Many analysts suggest that it is also showing signs of high volatility. The narrow trading range develops neither bullish nor bearish perspectives but only happens when there are competing narratives in the market.

The advantages of the range are –

• Easy to calculate without any advanced mathematical knowledge.
• Simple in interpretation and for comprehensive insights.
• It is used widely to state many results and information such as interest rate fluctuations, changes in production level, marks in a test, varying temperatures, weather forecasts, etc.
• In trading, it reflects the volatility and risk associated with a stock price movement.
• It is used for quality control purposes in different areas of work and studies.

The disadvantages of the range are –

• It depends on and is highly sensitive to the sample used from the whole dataset.
• It does not take account of all the values in the series.
• It cannot be calculated for open-end series.
• Do not encourage or support further algebraic or mathematical calculations.

### Range vs Interquartile Range

Distinguishing between the following concepts involves understanding their unique characteristics and applications. Let us understand them.

• It is the difference between the highest and lowest value or observation in a data set. In contrast, the interquartile range is the gap between the largest and smallest quartile in a data set.
• It does not divide the dataset, but the interquartile range is observed from the four groups, each representing 25% of the total observations.
• It defines the variance bracket between the highest and lowest observations, but the interquartile range is the variability measured around the median.

### Range vs Standard Deviation

When comparing the following concepts, it’s essential to recognize their fundamental distinctions and respective roles in statistical analysis.

• It is just the distance between the highest and lowest data points in a dataset. In comparison, the standard deviation is the square root of the variance.
• It is easy to calculate compared to the standard deviation of any dataset.
• It reflects how far the highest and lowest values in a dataset are, but standard deviation indicates how spread out the data is from its mean.

What is the difference between mean and range?

The difference between a mean and a range is that the former can only be calculated if there is a range provided, which means a bracket of quantitative values. Still, the core distinguishing factor is that the mean is the average of the range, but the latter is the difference between the highest and lowest values.

How range and volatility are connected?

The volatility of any element, factor, or, more commonly, stock is usually depicted and interpreted by range. So, suppose there is a stock; it will be determined by calculating the gap between its high and low prices on any given day, but at the same time, it elaborates the stock’s volatility. A significant value points to high volatility; conversely, a small value reflects low volatility.

How long is a range in trading?

An investor can look for a stock’s trading range for different time frames, so there is no specific period to opt for in the charts; it can be seen for all time frames. A typical short-term five-minute chart to a long-term daily or weekly price chart.

This article has been a guide to Range and its definition. We explain its formula, examples, comparison with interquartile range & standard deviation, & advantages. You may also find some useful articles here –