Use the data set and the indicated number of classes to construct


(c) a frequency polygon,

Pulse Rates
Number of classes: 6 Data set: Pulse rates of all students in a class 68 105 95 80 90 100 75 70 84 98 102 70 65 88 90 75 78 94 110 120 95 80 76 108

Verified step by step guidance

1. Step 1: Organize the data by first determining the range. Find the minimum and maximum pulse rates from the data set. The range is calculated as \(\text{Range} = \text{Maximum value} - \text{Minimum value}\).
2. Step 2: Calculate the class width by dividing the range by the number of classes (6). Use the formula \(\text{Class width} = \frac{\text{Range}}{6}\). Round up to a convenient number if necessary to cover the entire data range.
3. Step 3: Create the class intervals starting from the minimum value, adding the class width to form each subsequent class. Make sure the classes do not overlap and cover all data points.
4. Step 4: Tally the data points into each class interval to find the frequency for each class. This will give you the frequency distribution needed for the frequency polygon.
5. Step 5: To construct the frequency polygon, plot the midpoints of each class interval on the x-axis and their corresponding frequencies on the y-axis. Connect the points with straight lines, and remember to start and end the polygon at the baseline (frequency zero) by adding points before the first class midpoint and after the last class midpoint.

Key Concepts

Frequency Distribution and Class Intervals

A frequency distribution organizes data into classes or intervals, showing how many data points fall into each class. Determining appropriate class intervals, especially the number of classes, helps summarize data effectively and prepares it for graphical representation like histograms or frequency polygons.

Frequency Polygon Construction

A frequency polygon is a line graph that connects midpoints of class intervals plotted against their frequencies. It visually represents the distribution shape and trends in the data, making it easier to compare datasets or observe patterns compared to histograms.

Data Grouping and Midpoint Calculation

Grouping raw data into classes requires calculating class boundaries and midpoints. Midpoints are the average of the lower and upper class limits and serve as the x-coordinates in a frequency polygon, linking frequency data points smoothly to depict the distribution.