The IQ scores of ten students randomly selected from an...

The IQ scores of ten students randomly selected from an elementary school for academically gifted students are given. $$ \begin{array}{lllll} 133 & 140 & 152 & 142 & 137 \\ 145 & 160 & 138 & 133 & 138 \end{array} $$ Grouping the measures by their common hundreds and tens digits, construct a stem and leaf diagram, a frequency histogram, and a relative frequency histogram.

The IQ scores of ten students randomly selected from an elementary school for academically gifted students are given.
$$
\begin{array}{lllll}
133 & 140 & 152 & 142 & 137 \\
145 & 160 & 138 & 133 & 138
\end{array}
$$
Grouping the measures by their common hundreds and tens digits, construct a stem and leaf diagram, a frequency histogram, and a relative frequency histogram.

Key Concepts

Stem and Leaf Diagram

A stem and leaf diagram is a graphical tool that organizes data by dividing each value into a stem (typically the leading digits) and a leaf (usually the final digit). It preserves the original data points while simultaneously displaying the distribution, making it easier to identify shapes like symmetry, clusters, gaps, or outliers within a dataset.

Frequency Histogram

A frequency histogram is a type of bar graph where the x-axis represents intervals (or bins) of data values and the y-axis represents the counts or frequencies of data falling into each interval. It is used to summarize and visualize the distribution of a dataset, highlighting how frequently certain ranges of values occur.

Relative Frequency Histogram

A relative frequency histogram is similar to a frequency histogram but shows the proportion or percentage of the total number of data points within each interval instead of the raw count. This type of histogram is useful for comparing distributions, especially when datasets differ in size, by normalizing the frequencies for easier interpretation.

Grouping Data

Grouping data involves organizing individual data points into intervals or classes based on common characteristics, such as a shared set of leading digits. This process simplifies data analysis and visualization by reducing variability and highlighting patterns, trends, or clusters in the dataset.

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