Maharashtra Board Class 10 Maths Part I Chapter 6 Statistics PDF Download

Statistics

Statistics is useful in many fields of life: for example, agriculture, economics, commerce, medicine, botany, biotechnology, physics, chemistry, education, sociology, administration etc. An experiment can have many outcomes. To assess the possibility of possible outcomes, one has to carry out the experiment on a large scale and keep the record meticulously. Possibilities of different outcomes can be assessed using the record. For this purpose, rules are formulated in statistics.

Francis Galton (1822-1911) has done much of fundamental work in statistics. He used to prepare questionnaires, distribute them among people and request them to fill them up. He collected information from a number of people and recorded their backgrounds, financial situations, likes and dislikes, health etc. on a large scale. By that time, it was known that the fingerprints of different people are different. He collected finger-prints of a large number of people and invented a method of their classification. Using statistical methods, he showed that the possibility of finger prints of two different people being identical is nearly zero. This result made it possible to identify a person from his finger-prints. This method of identifying criminals was accepted in the judiciary. He had done much work in the field of anthropology of humans and other animals also.

Let's Recall

We usually find a specific property in the numerical data collected in a survey that the scores have a tendency to cluster around a particular score. This score is a representative number of the group. The number is called the measure of central tendency.

In the previous standards we have studied the measures of central tendency, namely the mean, median and mode, for ungrouped data.

Let's Study

Measures of central tendency - mean, median and mode from grouped frequency table.

Graphical representation of statistical data - histogram, frequency polygon, pie diagram

Teacher's Note

Central tendency helps us find the middle value. In India, when we say average height of students, we use mean.

Exam Trick

Remember: Mean = average, Median = middle value, Mode = most common. Think of mode like "most fashionable" - the one that appears most often!

Points to Remember

Mean is the sum of all scores divided by total scores.
Median divides data into two equal parts.
Mode is the score that repeats the most.
These three measures show us the center of data in different ways.
We choose which one to use based on what we need to find.

Activity 1

Measure the height in cm of all students in your class. We find that the heights of many students cluster near a specific number.

Activity 2

Collect a number of fallen leaves of a peepal tree. Distribute the leaves among the students and ask them to measure the lengths of them. Record the lengths. We notice that their lengths tend to cluster around a number.

Now we are going to do some more study of the mean, median and mode. Let us know the symbols and the terminology required for it.

The mean of statistical data = \[\frac{\text{The sum of all scores}}{\text{Total no. of scores}} = \frac{\sum_{i=1}^{N} x_i}{N}\]

(Here \(x_i\) is the i th score)

Mean is denoted by \(\overline{X}\) and it represents the average of the given data.

\[\overline{X} = \frac{\sum_{i=1}^{N} x_i}{N}\]

Let's Learn

Mean From Classified Frequency Distribution

When the number of scores in a data is large, it becomes tedious to write all numbers in the above formula and take their sum. So we use some different methods to find the sum.

Sometimes, the large data collected from an experiment is presented in a table in the grouped form. In such a case, we cannot find the exact mean of statistical data. Hence, let us study a method which gives the approximate mean, or a number nearby.

Direct Method

Let us study the method by an example.

Ex. : The following table shows the frequency distribution of the time required for each worker to complete a work . From the table find the mean time required to complete the job for a worker.

This is a preview of the first 3 pages. To get the complete book, click below.