Answer :
a. Frequency Distribution, Relative Frequency Distribution, and Cumulative Frequency Distribution with Five Classes:
Class Interval: 67-68, 69-70, 71-72, 73-74, 75-76
Frequencies: 4, 9, 9, 6, 2
Relative Frequencies: 13.33%, 30%, 30%, 20%, 6.67%
Cumulative Frequencies: 4, 13, 22, 28, 30
b. Frequency Histogram with Five Classes: A histogram with five bars representing the frequencies in each class interval.
c. Relative Frequency Histogram with Five Classes: A histogram with five bars representing the relative frequencies in each class interval.
d. Frequency Polygon with Five Classes: A polygon connecting the midpoints of the class intervals with the corresponding frequencies.
e. Ogive with Five Classes: A graph showing the cumulative frequencies plotted against the upper class boundaries, connected by line segments to form an ogive.
Let's analyze the given data and construct the requested statistical representations step by step.
a. Frequency Distribution with Five Classes:
To create a frequency distribution, we first need to determine the range of the data and calculate the class width:
Range = Max Height - Min Height = 74 - 67 = 7 inches
Class Width = Range / Number of Classes = 7 / 5 = 1.4 inches (round up to 2 inches for convenience)
Now, we'll create the frequency distribution table:
Class Interval Frequency
67 - 68 4
69 - 70 9
71 - 72 9
73 - 74 6
75 - 76 2
b. Frequency Histogram with Five Classes:
In the histogram, the x-axis represents the class intervals, and the y-axis represents the frequency.
You'll create bars above each class interval with heights corresponding to the frequency.
Make sure the bars are adjacent to each other since the classes don't overlap.
c. Relative Frequency Histogram with Five Classes:
To create the relative frequency histogram, divide each frequency by the total number of data points (30) and multiply by 100 to get percentages. Then, create the histogram as in part b, using these percentages on the y-axis.
d. Frequency Polygon with Five Classes:
To construct a frequency polygon, plot the midpoints of each class interval on the x-axis and the corresponding frequencies on the y-axis. Connect the points with line segments.
e. Ogive with Five Classes:
To create an ogive, first, calculate the cumulative frequencies. Starting with the lowest class interval, add each frequency to the previous cumulative frequency.
Then, plot the cumulative frequencies against the upper class boundaries on the x-axis. Connect the points with a line to form the ogive.
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