maths > statistics-basics

Predicting using Grouped Data : Probability

what you'll learn...

overview

In this page, finding probability of grouped data is explained with some examples.

predicting

Consider the data height of students in a class of $20$$20$ students.

$90.2$$90.2$, $97.4$$97.4$, $99.7$$99.7$, $88.3$$88.3$, $90.7$$90.7$

$93.5$$93.5$, $96.8$$96.8$, $89.5$$89.5$, $99.5$$99.5$, $98.9$$98.9$

$91.2$$91.2$, $101.3$$101.3$, $94.0$$94.0$, $93.4$$93.4$, $93.1$$93.1$

$94.7$$94.7$, $96.9$$96.9$, $92.8$$92.8$, $91.8$$91.8$, $99.6$$99.6$

The figure shows the grouped data with ranges less than $90$$90$, $90$$90$ to $95$$95$ range, $95$$95$ to $100$$100$ range, and greater than $100$$100$.

Considering this to be representative data for students of that age group, We try to predict the height of a student.

The probability of a random student in the height range $95$$95$ to $100$$100$ $=5/20$$= 5 / 20$

The probability of a random student of that age group in each of the range is given in the table.

zero probability

The probability of a random student to be exactly $97$$97$cm high is 0. It is noted that the probability of getting one particular value is $0$$0$ in continuous distribution. This will be explained in detail in higher classes.

different representation

Consider the data height of students in a class of $20$$20$ students.

$90.2$$90.2$, $97.4$$97.4$, $99.7$$99.7$, $88.3$$88.3$, $90.7$$90.7$

$93.5$$93.5$, $96.8$$96.8$, $89.5$$89.5$, $99.5$$99.5$, $98.9$$98.9$

$91.2$$91.2$, $101.3$$101.3$, $94.0$$94.0$, $93.4$$93.4$, $93.1$$93.1$

$94.7$$94.7$, $96.9$$96.9$, $92.8$$92.8$, $91.8$$91.8$, $99.6$$99.6$

The figure shows the grouped data with ranges less than $90$$90$, $90$$90$ to $95$$95$ range, $95$$95$ to $100$$100$ range, and greater than $100$$100$.

It is noted that, This is one possible grouping and the data can be grouped in different ranges.

A dirrerent grouping is applied and the data is provided in the table.

Probability of the same is given in the figure.

summary

Probability in Grouped Data : Probability is computed for of a range of values in grouped data. Probability of a range equals, the number of occurances in the range, divided by, the number of occurances in the data.

Outline