In Problems 13-16, use the frequency distributions in the...

In Problems $13-16,$ use the frequency distributions in the problem indicated from Section 2.2 to do the following: (a) Construct a cumulative frequency distribution. (b) Construct a cumulative relative frequency distribution. (c) Draw a frequency polygon. (d) Draw a frequency ogive. (e) Draw a relative frequency ogive. Problem 32

In Problems $13-16,$ use the frequency distributions in the problem indicated from Section 2.2 to do the following:
(a) Construct a cumulative frequency distribution.
(b) Construct a cumulative relative frequency distribution.
(c) Draw a frequency polygon.
(d) Draw a frequency ogive.
(e) Draw a relative frequency ogive.
Problem 32

Key Concepts

Frequency Ogive

A frequency ogive is a cumulative frequency graph that plots the cumulative total of frequencies against the upper boundary of each class interval. It is particularly useful for identifying median, quartiles, and percentiles in the data.

Relative Frequency Ogive

This graph plots cumulative relative frequencies (or percentages) against class boundaries, offering a visual tool for assessing the cumulative distribution of data relative to the whole data set. It allows for quick evaluation of the proportion of data that falls below a particular value.

Frequency Polygon

A frequency polygon is a graphical representation that connects points representing the midpoints of class intervals on the horizontal axis with the corresponding frequencies on the vertical axis. It provides a clear visualization of the distribution shape and trends.

Cumulative Relative Frequency Distribution

Similar to a cumulative frequency distribution but expressed in percentages or proportions rather than raw counts, a cumulative relative frequency distribution shows the cumulative proportion of observations within each class. It is essential for comparing datasets of different sizes and for assessing the overall data spread.

Cumulative Frequency Distribution

This concept involves summing the frequencies of classes sequentially, starting from the first interval, to show the number or proportion of observations that fall below the upper boundary of each class. It is useful for understanding how data accumulates and for determining median and percentile values.

Frequency Distribution

A frequency distribution organizes data into classes or intervals and shows how often each value or range of values occurs. It serves as a basic tool for summarizing and visualizing a data set, providing insights into the data’s overall pattern and distribution.

Transcript

00:01 Hello viewers, our today's question is from the topic of summarizing and organizing data.

00:06 Now we are given a data set for which we need to use frequency distribution and construct a cumulative frequency distribution, cumulative frequency distribution, cumulative frequency archive.

00:23 Now in order to obtain the class frequency distribution, we have divided the given data into class and worlds such as 4 to 8, 8 to 12, 12 to 16, 16 to 20, 20 to 24, 24 to 28 respectively.

00:37 There is only one tata point which lies in the interval 4 is to 8 and the others are distributed as shown.

00:43 Resulting which we get the cumulative frequency of the class 8 to 12 equal to 1 plus 14 which is equal to 15.

00:58 The table that depicts the cumulative frequency of all the classes will be given as follows.

01:07 Now, relative frequency distribution is a distribution of the observation and the corresponding relative frequencies.

01:15 It is defined as a number of times the values occur divided by the number of observations in the data set.

01:22 Now consider n is the frequency and capital n is a total of the frequency.

01:26 The relative frequency for a given data set will thus be equal to 0 .02.

01:36 The table that depicts the cumulative relative frequency of the distribution of the given data will be as follows.

01:45 Also, the frequency polygon which is a graph that represents the frequency of the data set, will be drawn by taking the plot class midpoint on x -axis and warn frequency for the 2...

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