Final answer:
Constructing a frequency distribution and a histogram involves grouping data into equal-width intervals and then representing the frequency of each group with a bar. Scales on axes must be chosen to appropriately represent data values. Relative frequency is calculated by dividing the occurrence of an event by the total number of events, useful for probability distributions.
Step-by-step explanation:
Constructing a frequency distribution involves organizing data into groups and counting how often each group occurs. To create a histogram, first, decide on the number of intervals or 'bins'. Typically, five to six intervals are adequate for a clear visualization. Divide the range of data into these equal-width intervals. Then, using a ruler and a pencil, sketch a histogram by drawing bars for each interval where the height of the bar represents the frequency of data within that interval. Ensure to scale the axes appropriately to reflect the data's range and frequency values.
For creating a frequency polygon, you must first have a frequency distribution. Then, plot points at the top center of each bar in the histogram corresponding to the frequency of each interval. Connect these points with straight lines, and you end up with a polygon. This method can be applied to visually represent the distribution for more specific data such as the 50 highest-ranked countries for depth of hunger.
To compute the relative frequency, divide the number of times a particular event occurs by the total number of events. For example, if you simulate picking diamonds from a deck with a calculator or actual playing cards, you would record these outcomes and then calculate the relative frequency for each outcome, which could later be used to find the expected value and standard deviation.
Finally, when interpreting the histogram, it allows you to analyze the data's approximate distribution visually. By looking at the shape, you can describe the distribution's characteristics, such as its skewness, modality, and spread.