Statistics Chapter 4.1

A list of numbers arranged in numerical order (smallest to largest or largest to smallest).

The middle number when a list of numbers has an odd number of values.

The mean (average) of the two middle numbers when a list has an even number of values.

The number that appears most often in a list of numbers.

When no number appears more often than others in a list.

An average where different data points have different levels of importance (weights).

Calculating an average where different data points have different levels of importance. For example, calculating a grade where tests and final exams have different weights.

To find the middle number after arranging a list of numbers in order when the list has an odd number of values.

The branch of statistics focused on organizing, summarizing, and presenting data.

The branch of statistics that interprets data and draws conclusions about a larger population.

Values that represent the 'center' or typical value of a set of data.

The sum of all values in a set divided by the total number of values.

Population: The entire group of interest. Sample: A smaller subset taken from the population.

The average of a set of values taken from a sample.

The average of all values in an entire population.

The middle value in a sorted set of numbers. If there are two middle values, it's their average.

The difference between the highest and lowest values in a dataset. It measures how spread out the data is.

A measure of how much data points typically deviate from the average (mean). A high standard deviation means data is widely spread, and a low one means it's clustered around the average.

To understand how spread out or concentrated the data is. It helps us see if the data is tightly clustered around the average or widely spread.

The range is based on only the two most extreme values. Just one outlier can drastically change the range.

Always 0. This is because positive and negative deviations cancel each other out.

Because the sum of deviations is always 0, squaring them eliminates the negative values and gives a non-zero value to represent spread.

When a quick estimate of data spread is needed and outliers are less of a concern.

When a more accurate and stable measure of data dispersion is needed, especially when outliers might exist.

A mathematical symbol () used to represent the sum of all values in a set of numbers.

A list of numbers arranged in numerical order, either from smallest to largest or largest to smallest.

The number that appears most frequently in a list.

An average where different data points have different levels of importance.

To calculate an average where some values are more important than others, like in a course grade where the final exam has a higher weight.

Identify the number that appears most often in the dataset. If no number repeats, there is no mode.

Multiply each data point by its weight, sum the results, and then divide by the sum of the weights.

The range (R) is a measure of how spread out data is. It's calculated as the difference between the maximum and minimum values in a dataset: R = MAX - MIN.

The range is sensitive because it relies entirely on the two most extreme values in the dataset. A single outlier can significantly alter the range, making it a less reliable measure of dispersion sometimes.

The sum of deviations from the mean is always 0, because positive and negative deviations cancel each other out. Squaring the deviations eliminates the negative values and ensures a non-zero value that reflects the overall spread of the data.

The range is useful when a quick estimate of data spread is needed and outliers are less of a concern. It provides a simple way to understand the overall 'spread' of a dataset.

Use standard deviation when you require a more accurate and stable measure of data dispersion, especially when outliers might exist. It considers all data points and provides a more reliable representation of the data's spread around the average.

Standard deviation is a more precise measure of dispersion, especially when outliers exist. It represents how much data points typically deviate from the mean.