Important Formulas Data Handling - (Maths) Class 8

Understanding Data

What is data?

• A systematic record of facts or different values of a quantity is called data.
• Data available in an unorganised form is called raw data.

Features of data

• Arranging data in an order to study their salient features is called presentation of data.
• Frequency gives the number of times that a particular entry or value occurs in the data.
• A table that shows the frequency of different values in the given data is called a frequency distribution table.
• A table that shows the frequency of groups (ranges) of values in the given data is called a grouped frequency distribution table.
• The groups used to group the values in given data are called classes or class intervals.
• The number of units that each class contains is called the class size or class width.
• The lower value in a class is called the lower class limit. The higher value in a class is called the upper class limit.
• The class having the greatest frequency is called the modal class; most observations will fall in the modal class.

Graphical representation of data

Bar graph

A bar graph is a pictorial representation of data in which rectangular bars of uniform width are drawn with equal spacing between them on one axis (usually the x-axis). The value of the variable is shown on the other axis (the y-axis). Each bar represents a category or a value and its height (or length) represents the frequency or amount.

Histogram

A histogram is used to represent grouped numerical data. The class intervals are shown on the horizontal axis and the heights of adjacent bars represent the frequencies of those class intervals. There is no gap between the bars because class intervals are continuous and adjacent.

Circle graph or Pie-chart

A circle graph or pie-chart shows the relationship between a whole and its parts. The whole circle represents the total and each sector (slice) represents a part proportional to its share in the total.

Important concepts and formulas

Basic terms

• Frequency (f): Number of observations in a class or for a value.
• Cumulative frequency (cf): Running total of frequencies up to and including a given class or value.
• Class mark (m): Midpoint of a class interval. m = (lower class limit + upper class limit) ÷ 2.
• Class width (h): Difference between the upper and lower class limits of a class. h = upper class limit − lower class limit.
• Range: Difference between the maximum and minimum values in the data. Range = Maximum − Minimum.
• Organising data: ​To draw meaningful conclusions from data, it must be arranged in a clear and systematic way. Well-organised data helps us compare values, observe patterns and make decisions.
• Experiments with equal chance: ​Some experiments have outcomes that all have the same likelihood of occurring. These are situations where no outcome is favoured over another.
• Random experiment: A random experiment is one in which the exact outcome cannot be predicted in advance, even though all possible outcomes are known.
• Equally likely outcomes: Outcomes are equally likely when each has the same chance of happening. For example, getting heads or tails when tossing a fair coin.
• Probability of an event: Probability measures the chance of an event occurring.
  Probability = Number of favourable outcomes ÷ Total number of possible outcomes
  This formula applies when all outcomes are equally likely.
• Event: An event is one or more outcomes of an experiment. For example, getting an even number when rolling a die.
• Probability in real life:  Ideas of chance and probability help us understand everyday situations such as weather forecasts, games, predictions and decision-making.