Mean, median, mode, and range: find the missing number

Learning Objectives Calculate a missing value in a data set when the mean is provided. Determine a missing value in an ordered data set when the median is provided. Identify a missing value in a data set when the mode is specified. Find a missing value in a data set when the range is given. Apply algebraic reasoning to solve for unknown data points in statistical problems. Verify their calculated missing values by re-calculating the given statistic. Ever wondered how statisticians figure out missing pieces of information when they only have averages or spreads? 🤔 We're about to become data detectives! In this lesson, you'll learn how to use your knowledge of mean, median, mode, and range to find a missing number in a data set. This skill is crucial for understand...

TermDefinitionExample MeanThe average of a data set, found by summing all values and dividing by the number of values.For the data set {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 ascending order. If there's an even number of values, it's the average of the two middle values.For {1, 3, 5, 7, 9}, the median is 5. For {1, 2, 3, 4}, the median is (2+3)/2 = 2.5. 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 {5, 5, 6, 7, 7}, the modes are 5 and 7. RangeThe difference between the highest and lowest values in a data set.For {10, 15, 20, 25}, the range is 25 - 10 = 15. Data SetA collection of numbers or values,...

Mean Formula $\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$ Use this formula to calculate the mean or to find a missing value when the mean and other values are known. You can rearrange it to find the sum of values: $\text{Sum of all values} = \text{Mean} \times \text{Number of values}$. Median Determination For an odd number of values, the median is the middle value after ordering. For an even number of values, the median is the average of the two middle values after ordering. To find a missing number using the median, first order the known values. The position of the missing number will affect which value(s) become the median. Mode Identification The mode is the value that appears with the highest frequency in the data set. If a mode is gi...