Data Handling - Mean, Median, and Mode

Data is a collection of facts, such as numbers, words, or measurements, gathered to provide information. We often organize data into tables or tally charts, where each tally mark $|$ represents one item and a diagonal line across four marks $||||$ signifies a group of five, making it easier to count visually.

The Mean, often called the 'Average', represents the value each item would have if the total were shared equally. Imagine having four different stacks of blocks; the mean is the height the stacks would be if you moved blocks around until every stack was exactly the same height.

The Median is the middle value in a set of data that has been arranged in order from smallest to largest. If you look at a set of five numbers, the median is the third number, sitting exactly in the center like the nose on a face, with an equal number of values on its left and right.

The Mode is the value that appears most frequently in a data set. On a bar graph, the mode is the category with the tallest bar. A data set can have more than one mode if multiple numbers appear with the same highest frequency, or no mode at all if every number appears only once.

The Range is the difference between the highest and the lowest values in a data set. It describes how spread out the numbers are. Visually, it is the distance between the two ends of a data set when plotted on a number line, calculated by subtracting the smallest number from the largest.

Ordering Data is the process of arranging numbers in ascending order (from smallest to largest) or descending order (from largest to smallest). This is a crucial visual step before identifying the median or range, much like lining up students by height for a class photo.

Frequency refers to how many times a particular value occurs in a data set. When we create a frequency table, we use numbers to show the total count of each item, helping us quickly identify the mode without having to count through a long list of raw data.