Question

Describe the difference between discrete and continuous data with examples. (5)

What is the difference between the process of using probability calculations for discrete verses continuous data? How do these calculations change? (5)

Answer 1

Difference between discrete and continous data

Discrete data is the type of data that has finite or countable infinite values. But continuous data is the data falls in a continuous sequence.

For eg. The data on the number of children in a family is discrete, while the data on the weight or hight of these children is continuous.

Discrete data is countable while continuous data is measureable. For eg., we count the number of mangoes on a mango tree, while measure the weight of each mango.

Discrete data represented graphically by bar graphs, while continous represented by histograms

Tabulation of discrete data is done as ungrouped frequency table, and some times they may be grouped, But continuous data can be tabulated only in the form of grouped frequency distribution.

Probability calculations for discrete and continuous data

For a discrete data, we can identify the possible values of the variable and form the data collected we can identify the frequency of each possible value out of the total number of observations. The ratio of frequency of each value of the variable to the total number of observations is considered as the probability of happenning that value.

These probability masses at various possible valued of the discrete data can be summarised in a mathematical form called probability mass function. We answer any probability question regarding this discrete data using its probability mass function by addition.

While in case of continuous variable, the frequency of data appeared in certain classes(intervals) is recorded and the proability of the value of happen in that interval is approximated as the ratio of the frequncy of data in that interval to the totall observations. Probability for a particular value is treated as zero. Using the various probabililties for the variable in various intervals, a mathematical function called probabaility density function is identified. We use this probability density function to identify the probability of the happenning of the value in a given interval, using the techniques of clculus like integration.

As described above, summation is used in probability calculation of discrete data, while in the case of continuous data infinite summation, that is integration is used in probability calculations.