The diameter of 100 piston rings are measured and recorded...

The diameter of 100 piston rings are measured and recorded as follows: $$ \begin{array}{|c|c|} \hline \text { Diameter } d(\mathrm{~mm}) & \text { Frequency } \\ \hline 86.00 \leq d<86.10 & 9 \\ 86.10 \leq d<86.15 & 9 \\ 86.15 \leq d<86.25 & 12 \\ 86.25 \leq d<86.40 & 15 \\ 86.40 \leq d<86.45 & 10 \\ 86.45 \leq d<86.50 & 7 \\ 86.50 \leq d<86.70 & 20 \\ 86.70 \leq d<87.00 & 18 \\ \hline \end{array} $$ Draw a histogram and a frequency polygon for this data.

The diameter of 100 piston rings are measured and recorded as follows:
$$
\begin{array}{|c|c|}
\hline \text { Diameter } d(\mathrm{~mm}) & \text { Frequency } \\
\hline 86.00 \leq d<86.10 & 9 \\
86.10 \leq d<86.15 & 9 \\
86.15 \leq d<86.25 & 12 \\
86.25 \leq d<86.40 & 15 \\
86.40 \leq d<86.45 & 10 \\
86.45 \leq d<86.50 & 7 \\
86.50 \leq d<86.70 & 20 \\
86.70 \leq d<87.00 & 18 \\
\hline
\end{array}
$$
Draw a histogram and a frequency polygon for this data.

Key Concepts

Frequency Polygon

A frequency polygon is a line graph created by plotting points that represent the frequency of data within each class interval at the midpoints of those intervals and then connecting these points with straight lines. This method of data visualization provides a clear picture of the distribution shape and is particularly useful for comparing multiple data sets on the same graph.

Histogram

A histogram is a graphical representation of data where the data are grouped into ranges, also known as bins or class intervals. The height of each bar reflects the frequency or count of data points within that range. Histograms are useful for visualizing the distribution, central tendency, and spread of continuous data, making it easier to identify skewness, modality, and outliers.

Grouped Data

Grouped data refers to data that has been organized into categories or intervals, known as class intervals, which summarize a large number of individual observations. This process helps in simplifying the data set for further analysis and visualization, such as creating histograms or frequency polygons.

Class Intervals

Class intervals are the ranges into which continuous data are divided for analysis in a grouped frequency distribution. These intervals should be mutually exclusive and collectively exhaustive, ensuring that every data point is included in one, and only one, interval. Proper selection of class intervals is crucial for accurately representing the distribution of data.

Transcript

Please give Ace some feedback