The frequency distribution shows the waiting times (in...

The frequency distribution shows the waiting times (in minutes) for 50 patients at a walk-in medical facility, Construct a histogram, frequency polygon, and ogive for the data. Is the distribution skewed? How many patients waited longer than 30 minutes? $$ \begin{array}{lr} \text { Class limits } & \text { Frequency } \\ \hline 11-15 & 7 \\ 16-20 & 9 \\ 21-25 & 15 \\ 26-30 & 9 \\ 31-35 & 5 \\ 36-40 & 3 \\ 41-45 & \frac{2}{2} \\ & \text { Total } 50 \end{array} $$

The frequency distribution shows the waiting times (in minutes) for 50 patients at a walk-in medical facility, Construct a histogram, frequency polygon, and ogive for the data. Is the distribution skewed? How many patients waited longer than 30 minutes?
$$
\begin{array}{lr}
\text { Class limits } & \text { Frequency } \\
\hline 11-15 & 7 \\
16-20 & 9 \\
21-25 & 15 \\
26-30 & 9 \\
31-35 & 5 \\
36-40 & 3 \\
41-45 & \frac{2}{2} \\
& \text { Total } 50
\end{array}
$$

Key Concepts

Skewness

Skewness refers to the asymmetry in a data distribution. A distribution is said to be skewed when one tail is longer or fatter than the other. Understanding skewness is crucial for interpreting the underlying patterns in data, as it affects the mean, median, and mode’s relationship.

Ogive

An ogive, or cumulative frequency graph, plots the cumulative frequency against the upper class boundary of each interval. It is used to determine the number or proportion of observations below a particular value, which aids in identifying percentiles and median values.

Cumulative Frequency

Cumulative frequency is the running total of frequencies through the classes in a frequency distribution. It helps determine the number of observations that fall below or above a certain threshold, which is useful for answering questions such as how many patients waited longer than a specific time.

Frequency Polygon

A frequency polygon is a line graph obtained by connecting the midpoints of the top of the bars of a histogram. It provides a clear visualization of the distribution's overall shape and trends, and it is particularly useful for comparing multiple distributions over the same intervals.

Group (or Class) Intervals

In grouped data analysis, individual data points are divided into intervals known as classes. These intervals consolidate data values into meaningful ranges, allowing for a more manageable comparison and visualization of the data distribution.

Frequency Distribution

A frequency distribution is a summary of data showing the number of observations within different intervals or categories. It helps in organizing large data sets by grouping individual scores into classes, making it easier to see patterns, trends, and the overall shape of the data.

Histogram

A histogram is a graphical representation of a frequency distribution where data are grouped into specified intervals (bins) on the x-axis, and the height of each bar represents the frequency or count of data within that interval. It is useful for visualizing the shape of the data distribution and identifying patterns like skewness or gaps.

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