Q.Let us look at the following problems and select the suitable statistical technique to be applied (Mean/Median/Mode/Range/Standard Deviation):

Here are the suitable statistical techniques for each problem:

1. To understand the disparity or spread in salaries, Standard Deviation is the most appropriate measure. It quantifies the average amount by which individual salaries deviate from the mean salary.
2. To determine the average performance of a class in a test, the Mean is the most suitable technique. It provides a central value representing the overall performance.
3. To compare the typical height of residents between two cities, the Mean is generally used. Height data often follows a distribution where the mean is a good representative of central tendency.
4. To find the dominant or most frequently occurring value from a set of values, the Mode is the correct statistical technique. …

Descriptive statistics are fundamental tools in understanding and summarizing data. They help us describe the main features of a dataset, providing simple summaries about the sample and the observations that have been made. These techniques fall broadly into two categories: measures of central tendency, which tell us about the "typical" or "average" value, and measures of dispersion, which describe the spread or variability of the data.

Let's look at the common techniques:

• Mean: This is the arithmetic average, calculated by summing all values and dividing by the number of values. It's widely used for numerical data and represents a balanced point in the distribution. However, it can be heavily influenced by extreme values (outliers).
• Median: This is the middle value in a dataset when all values are arranged in ascending or descending order. If there's an even number of values, it's the average of the two middle values. The median is particularly useful when data might be skewed by outliers, as it is not affected by them.
• Mode: This is the value that appears most frequently in a dataset. It's the only measure of central tendency that can be used for categorical data (like colors or types of cars), and it indicates the most popular or common item.
• Range: This is the simplest measure of dispersion, calculated as the difference between the highest and lowest values in a dataset. It gives a quick idea of the total spread but is very sensitive to outliers.
• Standard Deviation: This is a more sophisticated measure of dispersion that quantifies the average amount of variation or dispersion of a set of data values around the mean. A low standard deviation indicates that data points tend to be close to the mean, while a high standard deviation indicates that data points are spread out over a wider range of values. It provides a comprehensive understanding of data spread.

Now, let's apply these techniques to the given problems:

1. The management of a company wants to know about disparity in salaries of all employees.

   • Suitable Technique: Standard Deviation
   • Explanation: The term "disparity" directly refers to the spread or variation in salaries. While the Range would give the difference between the highest and lowest salary, the Standard Deviation provides a much more robust and informative measure. It tells the management, on average, how much individual salaries deviate from the mean salary. A higher standard deviation would indicate greater disparity, meaning salaries are widely spread, while a lower standard deviation would suggest salaries are clustered more closely around the average.

2. Teacher wants to know about the average performance of the whole class in a test.

   • Suitable Technique: Mean
   • Explanation: When we talk about "average performance" for numerical data like test scores, the Mean is the most appropriate and commonly used measure. It provides a single value that represents the typical score of the class, giving the teacher a clear understanding of the overall academic standing.

3. Compare height of residents of two cities.

   • Suitable Technique: Mean (and potentially Standard Deviation) …