Measures Of Variability

Explanation
Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used to analyze data in order to make informed decisions and draw conclusions. Statistics helps in understanding patterns, trends, and relationships in data, making it a crucial tool for various fields such as economics, social sciences, and business.

Explanation
Scores typically form a bell-shaped curve on a graph. This is because in a large population, most scores tend to cluster around the average, with fewer scores at the extremes. The bell curve, also known as the normal distribution, is symmetrical, with the highest frequency of scores occurring at the mean and gradually decreasing as the scores deviate from the mean in either direction. This pattern is commonly observed in many natural phenomena and is a fundamental concept in statistics.

Explanation
Variability describes how far apart scores are spread in a distribution. It provides information about the dispersion or spread of data points. A high variability indicates that scores are spread out over a wide range, while a low variability suggests that scores are clustered closely together. Variability is an important measure in statistics as it helps to understand the distribution and characteristics of a dataset.

Explanation
The range is a measure of variability that represents the difference between the highest and lowest values in a dataset. It provides information about the spread or dispersion of the data points. By calculating the range, one can determine the extent to which the values deviate from each other, helping to understand the overall variability in the dataset.

Explanation
The range is calculated by subtracting the lowest score from the highest score. In this context, the missing word should be "lowest" to complete the sentence. The range represents the spread or variability of the scores, and it is obtained by considering the extreme values, which are the highest and lowest scores.

Explanation
The highest score in the distribution of scores is 140.

Explanation
The lowest score in the given distribution of scores is 3. This can be determined by comparing all the numbers in the distribution and identifying the smallest value, which is 3.

Explanation
The range is calculated by subtracting the lowest value from the highest value in a set of numbers. In this case, the lowest value is 20 and the highest value is 95. Subtracting 20 from 95 gives us a range of 75.

Explanation
The range is calculated by subtracting the smallest value from the largest value in a set of numbers. In this case, the smallest value is 4 and the largest value is 100. Therefore, the range is 100 - 4 = 96.