Changes in mean, median, mode, and range

Learning Objectives Define and calculate mean, median, mode, and range for a given data set. Predict how adding a new data point affects the mean, median, mode, and range. Predict how removing an existing data point affects the mean, median, mode, and range. Analyze how changing an existing data point affects the mean, median, mode, and range. Explain the impact of outliers on measures of central tendency and spread. Apply their understanding to interpret changes in real-world data scenarios. Ever wonder how a new player's score or a sudden sale affects a team's average or a store's typical price? 📊 Let's explore how data changes! In this lesson, you'll learn what happens to the mean, median, mode, and range of a data set when numbers are added, re...

TermDefinitionExample Data SetA collection of numbers or values related to a particular subject.The ages of students in a club: {12, 13, 12, 14, 13} MeanThe average of a data set, found by summing all values and dividing by the number of values.For {2, 4, 6}, the mean is (2+4+6)/3 = 12/3 = 4. MedianThe middle value in a data set when the values are arranged in order. If there are two middle values, the median is their average.For {2, 3, 5, 8, 9}, the median is 5. For {2, 3, 5, 8}, the median is (3+5)/2 = 4. ModeThe value that appears most frequently in a data set. A data set can have one mode, multiple modes, or no mode.For {1, 2, 2, 3, 4}, the mode is 2. For {1, 1, 2, 2, 3}, the modes are 1 and 2. RangeThe difference between the highest and lowest values in a data set. It measures the sp...

Calculating the Mean $ ext{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}$ To find the average, add up all the numbers and then divide by how many numbers there are. When data changes, either the sum or the count (or both) will change, requiring recalculation. Finding the Median 1. Order the data from least to greatest. 2. Find the middle value. If there's an odd number of values, it's the single middle number. If there's an even number, it's the average of the two middle numbers. When data is added or removed, the order of the data set might change, and the position of the middle value(s) will definitely change, requiring reordering and re-identifying the median. Identifying the Mode The mode is the value that appears mo...