Changes in mean, median, mode, and range

Learning Objectives Calculate the initial mean, median, mode, and range of a given data set. Predict and calculate the new mean, median, mode, and range after a data point is added or removed. Analyze how an outlier affects the mean and median differently. Determine the new mean, median, mode, and range when a constant value is added to or subtracted from every data point. Determine the new mean, median, mode, and range when every data point is multiplied or divided by a constant value. Solve for a missing data value required to achieve a specific mean. Ever wonder how one bad quiz score can dramatically drop your grade average? 📉 Let's investigate the math behind why that happens! This tutorial explores how measures of central tendency (mean, median, mode) and a meas...

TermDefinitionExample MeanThe arithmetic average of a data set. It is calculated by summing all the values and dividing by the count of values.For the data set {4, 6, 6, 8}, the mean is (4 + 6 + 6 + 8) / 4 = 6. MedianThe middle value in a data set that has been ordered from least to greatest. If there is an even number of values, the median is the average of the two middle values.For the ordered data set {3, 5, 8, 10}, the median is (5 + 8) / 2 = 6.5. ModeThe value that appears most frequently in a data set. A data set can have one mode, more than one mode (bimodal, multimodal), or no mode.For the data set {4, 6, 6, 8, 9}, the mode is 6. RangeA measure of spread, calculated as the difference between the maximum and minimum values in a data set.For the data set {3, 5, 8, 10}, the range is...

Effect of Adding/Subtracting a Constant (k) If you add or subtract a constant `k` to every value in a data set: New Mean = \bar{x}_{old} \pm k New Median = M_{old} \pm k New Mode = Mode_{old} \pm k New Range = R_{old} (unaffected) Use this rule when a uniform change is applied to all data points, like giving every student 5 bonus points. The measures of center shift by the constant, but the spread (range) remains the same because the distance between the highest and lowest values does not change. Effect of Multiplying/Dividing by a Constant (k) If you multiply or divide every value in a data set by a positive constant `k`: New Mean = \bar{x}_{old} \times k New Median = M_{old} \times k New Mode = Mode_{old} \times k New Range = R_{old} \times k Use this rule when sca...