Changes in mean, median, mode, and range

Learning Objectives Calculate the initial mean, median, mode, and range for a given dataset. Analyze how adding or removing a data point affects the mean, median, mode, and range. Predict the effect of an outlier on measures of central tendency and spread. Determine how adding a constant to every data point in a set changes its statistical measures. Determine how multiplying every data point in a set by a constant changes its statistical measures. Evaluate which measure (mean or median) is more resistant to change when outliers are introduced. Apply these concepts to solve problems involving data manipulation and interpretation. What happens to your class's average test score if the top student scores a perfect 100 on the next exam? 📈 Let's investigate! In this...

TermDefinitionExample MeanThe arithmetic average of a dataset, calculated by summing all values and dividing by the count of values.For the set {2, 3, 4, 7}, the mean is (2+3+4+7) / 4 = 4. MedianThe middle value in a dataset that has been ordered from least to greatest. If there are two middle values, the median is their average.For the ordered set {2, 3, 7, 8}, the median is (3+7) / 2 = 5. ModeThe value that appears most frequently in a dataset. A dataset can have one mode, more than one mode, or no mode.For the set {2, 3, 3, 4, 5}, the mode is 3. RangeA measure of spread, calculated as the difference between the maximum and minimum values in a dataset.For the set {2, 3, 7, 8}, the range is 8 - 2 = 6. OutlierA data point that is significantly different from the other data points in a set...

Rule 1: Effect of Adding a Constant (k) For a dataset {x_1, x_2, ..., x_n}, if a constant 'k' is added to each value, then: New Mean = Old Mean + k New Median = Old Median + k New Mode = Old Mode + k New Range = Old Range Use this rule when every data point is uniformly increased or decreased. Notice that the spread (range) of the data does not change. Rule 2: Effect of Multiplying by a Constant (c) For a dataset {x_1, x_2, ..., x_n}, if each value is multiplied by a constant 'c', then: New Mean = Old Mean * c New Median = Old Median * c New Mode = Old Mode * c New Range = Old Range * |c| Use this rule for scaling transformations, like percentage increases or unit conversions. Both central tendency and spread are affected.