Data Handling - Collection and Organisation of Data

Data Collection: Data is a collection of numbers gathered to give some information. Before collecting data, we must clearly define the purpose of the study. For example, to find the average height of students, we specifically collect height measurements in centimeters.

Organization of Data: Raw data is usually unorganized and hard to understand. To make sense of it, we use a Frequency Distribution Table. This table consists of columns for the observation, Tally Marks, and Frequency. Tally marks are vertical lines $|$ for numbers $1$ to $4$, and the fifth mark is a diagonal line across the first four $\cancel{||||}$ to represent a group of five.

Arithmetic Mean: The mean (or average) is the most common representative value of a data set. It is the central value that represents the whole group. Visually, it can be thought of as the 'leveling out' point of all numerical values in the set.

Range: The range is the measure of the spread of the data. It is calculated by subtracting the lowest observation from the highest observation. A large range indicates that the data points are spread widely apart, while a small range indicates they are clustered closely.

Mode: The mode is the value that occurs most frequently in the data set. In a frequency distribution table, the observation with the highest frequency is the mode. Visually, on a bar graph, the mode is represented by the tallest bar.

Median: The median refers to the value which lies in the middle of the data when the observations are arranged in increasing or decreasing order. Exactly half of the data points lie above the median, and half lie below it.

Bar Graphs: A bar graph is a visual representation of data using rectangular bars of uniform width. The height of each bar is proportional to the frequency it represents. In a bar graph, bars are drawn with equal spacing between them on the horizontal axis (X-axis), while the numerical values are plotted on the vertical axis (Y-axis).