## Short Questions and Answers about *Data Representation *

This page contains short questions and answers about numerical data representation methods such as Measure of Central Tendency, Measure of Dispersion, Measure of Position, Frequency Distribution etc.

**Frequency: ** The number of measurements in an interval of a frequency distribution is called frequency. The number of observations falling in a particular class is referred to as the class frequency or simply frequency and is denoted by *f*.

It is a record of how often each value (or set of values) of the variable in question occurs. It may be enhanced by the addition of percentages that fall into each category

*Steps in Frequency Distribution:*

Following are the basic rules to construct frequency distribution

- Decide the number of classes into which the data are to be grouped and it depends upon the size of data.
- Determine the RANGE (difference between the smallest and largest values in data) data.
- Decide where to locate the class limit (numbers typically use to identify the classes).
- Determine the reaming class limits by adding the class interval repeatedly.
- Distribute the data into classes by using tally marks and sum it in frequency column. Finally, total the frequency column to see that all data have been accounted for.

**Frequency:**

The number of observations falling in a particular class is known as class frequency or simply frequency.

**Frequency distribution:**

When we arrange the frequencies in a form of table then it is known as Frequency distribution.

There is no difference between cumulative frequency distribution and Cumulative Frequency Polygon, because the graph of cummulative frequency distribution is known as Cumulative Frequency Polygon/ogive.

There is no hard and fast rule for deciding on the number of classes. Number of classes actually depends on the size of data. Statistical experience tells us that no less than 5 and no more than 20 classes are generally used. Use of too many classes will defeat the purpose of condensation and too few will result in too much loss of information. Deciding on the number of classes does not depend on the value of range. To find class interval â€˜hâ€™ we should first find the range and divide it by number of classes.

The true class limits of a class are known as its class boundaries. It should be noted that the difference between the upper class boundary and the lower class boundary of any class is equal to the class interval. The problem with class intervals is the space between the intervals. To solve this problem, class boundaries are used. Class boundaries remove space between intervals by dividing it in half. One half is added to the upper limit of one interval and the other half is subtracted from the lower limit of the next interval. By subtracting the class interval from upper class boundary of first class we can find the lower class boundary of first class.

- Firstly we find the difference between the upper class limit of first class (group) and lower class limit of second class
- Secondly we divide that difference by two. Then we subtract that resulting value in each lower class limit of each class and add in upper class limit of each class in such a way we can make the class boundaries.

**Example:**For the data given below, we can make class boundaries easily.

**Data:**

Class Limits | Class Boundaries |
---|---|

3.5 to 4.4 | --- |

3.45 to 4.45 | --- |

4.5 to 5.4 | --- |

4.45 to 5.45 | --- |

5.5 to 6.4 | --- |

5.45 to 6.45 | --- |

Find the difference between 4.4 (upper class limit of first class) and 4.5 (lower class limit of second class), i.e. 4.5-4.4=0.1 Now divide the difference by 2 i.e. 0.1/2=0.05 Subtract this resulting value of 0.05 from 3.5 (lower class limit of first class); we will get 3.45. Add this resulting value of 0.05 in 4.4 (upper class limit of first class); we will get 4.45. For all classes continue this subtraction in lower class limit and addition in upper class limit of each class.

Cumulative frequency distribution: A cumulative frequency distribution is a plot of the number of observations falling in or below an interval. The graph shown here is a cumulative frequency distribution of the scores on a statistics test.

**Cumulative frequency **is used to determine the number of observations that lie above (or below) a particular value in a data set. The cumulative frequency is calculated using a frequency distribution table, which can be constructed from stem and leaf plots or directly from the data. We need to calculate cumulative frequency for finding median, mode and to draw cumulative frequency curves. The cumulative frequency is determined by adding each frequency from a frequency distribution table to the sum of its predecessors.