8th Class Mathematics Data Handling

Data Handling

• Data: The word data means information in the form of numerical figures or a set of given information.

• Raw data: Data obtained in the original form is called a raw data.

• Array: Arranging the numerical figures of a data in ascending or descending order is called an array.

• Tabulation: Arranging the data in a systematic tabular form is called tabulation or presentation of the data.

• Observation: Each numerical figure in a data is called an observation.

• Frequency: The number of times a particular observation occurs is called its frequency.

• Range: The difference between the highest and the lowest values of the observations in a given data is called its range.

• Frequency distribution: A table showing the frequencies of various observations of data is called a frequency distribution or simply a frequency table.

• Tally marks

(i) When the number of observations is large, we make use of tally marks to find the frequencies.

(ii) Tallies are usually marked in a bunch of five for the sake of easy counting.

• Grouped data

(i) When the list of observations is long, the data is usually organised into groups called class intervals and the data so obtained is called a grouped data.

(ii) The lower value of a class interval is called its lower limit and the upper value is called its upper limit.

(iii) The difference between the upper and lower class limits is called the width or the size of the class interval.

(iv) The mid-value of a class interval is called its class mark.

• Graphical representation

(i) Histogram: A histogram is a pictorial representation of the grouped data in which class intervals are taken along the horizontal axis and class frequencies along the vertical axis and for each class a rectangle is constructed with the class interval as the base and the class frequency as the height.

There is no gap between the bars in a histogram as there is no gap between the class intervals.

(ii) Bar graph: In a bar graph, bars of uniform width are drawn with various heights. The height of a column represents the frequency of the corresponding observation.

(iii) Double bar graph: A double bar graph shows two sets of data simultaneously. It is useful to compare data related to two variables.

• In a pie-chart, the values of different components are represented by the sectors of a circle. The total angle of \[{{360}^{o}}\] at the centre of a circle is divided according to the values of the components.

\[\operatorname{Central}\,\,angle\,for\,a\,\,component=\frac{Value\,of\,the\,component}{Total\,value} 36{{0}^{o}}\]

• Experiment: An experiment is a situation involving chance or probability that leads to results called outcomes.

• Outcome: An outcome is the result of a single trial of an experiment.

• Event: An event is one or more outcomes of an experiment.

• Probability: Probability is the measure of how likely an event is.

The probability of event A is the number of ways A can occur divided by the total number of possible outcomes.

\[\operatorname{P}\left( A \right)=\frac{The\,number\,of\,ways\,event\,A\,can\,occurr}{The\,total\,number\,of\,possible\,outcome{s}'}\]

when the outcomes are equally likely.

• Random experiment: A random experiment is one whose outcomes cannot be predicted exactly in advance.

• Equally likely outcomes: The outcomes of an event with the same probability of occurrence are known as equally likely outcomes,