Question

The dintribution in which mean, mediun, mode are equal is ...

Short answer

Normal distribution.

Step-by-step solution

Understand the Question

The question asks for the name of a distribution where the mean, median, and mode are equal. This requires knowledge of common statistical distributions and their properties.

Identify Distribution

Recall that the mean, median, and mode being equal is a characteristic of the normal distribution. This distribution is symmetric and its central tendency measures coincide at the center of the distribution.

Answer the Question

Given that the normal distribution is the one where the mean, median, and mode are equal, we can conclude that this is the answer.

Key concepts

Mean Median Mode Equality

In statistics, the mean, median, and mode are measures of central tendency that provide insights into the distribution of a data set. When these three measures are equal, it is a special characteristic of the normal distribution.

The **mean** is the average of all data points, calculated by summing all the values and dividing by the number of observations.

• The **median** is the middle value that separates the higher half from the lower half of the data set when it is ordered.
• The **mode** is the value that appears most frequently in a data set.

A normal distribution, also known as a Gaussian distribution, has a perfect balance about its center, leading the mean, median, and mode to coincide. This equality signifies that in a perfectly normal distribution, the central point (mean) has the highest frequency (mode) and divides the data into two equal halves (median).

Understanding this unique equality helps recognize a normal distribution, crucial for many statistical analyses.

Symmetric Distribution

A symmetric distribution is one that can be split down the middle so that the left and right halves mirror each other. This symmetry is a key property of the normal distribution, a common distribution in statistics which often arises naturally in data sets.

• In a symmetric distribution, if you fold the graph down the center, both sides will align perfectly.
• This implies that data is evenly distributed around the central value, typically the mean.

Symmetry in distribution ensures that the central tendency measures are aligned in the same direction, promoting the characteristic that the mean equals the median and the mode. Practically, this means that numbers are not skewed to either side, providing a clear and predictable picture of variability in your dataset.

Symmetry simplifies the analysis and interpretation of data, making it easier to predict probabilities and outcomes.

Central Tendency Measures

Central tendency measures are statistical metrics that describe the center of a data distribution. These measures include the mean, median, and mode, which serve different purposes and provide unique insights into the nature of the data.

• The **mean** offers a global perspective by averaging all values, showing the overall level.
• The **median**, as the middle value, provides a midpoint that divides the data into equal parts.
• The **mode** identifies the most common data point, revealing frequently occurring values.

In normal distributions, these measures coincide, highlighting the even spread of data and the absence of skewness.

Central tendency measures are fundamental in statistics because they offer concise summaries of data, helping in making inferences about a population based on a sample. Understanding these concepts aids in performing statistical analyses, facilitating the decision-making process based on data insights.