Problem Related To Steam & Leaf Display || Box & Whisker Plot || 2018 Spring || Business Statistics
Problem Related To Steam & Leaf Display || Box & Whisker Plot || 2018 Spring || Business Statistics
#steamandleafdisplay #businessstatistics #bba2ndyear
In business statistics, stem-and-leaf displays and box-and-whisker plots are two visual methods used to summarize and analyze the distribution of a dataset. Here's a brief description of each:
Stem-and-Leaf Display
A *stem-and-leaf display* (or plot) is a way to display quantitative data to show its distribution while retaining the original data points. It helps in identifying the shape of the data distribution and is especially useful for small datasets.
**Structure**: The stem-and-leaf plot separates each data point into a "stem" (the leading digit or digits) and a "leaf" (the trailing digit). For example, the number 47 would have a stem of 4 and a leaf of 7.
**How to Read**: The stems are listed vertically in ascending order, and the leaves are listed horizontally beside their corresponding stems. This allows you to quickly see the distribution of values, identify clusters, gaps, and outliers.
**Example**: If you have data points like 43, 47, 52, and 56, the stem-and-leaf plot would look like:
```
4 | 3 7
5 | 2 6
```
Here, the "4" and "5" are the stems, and the "3, 7" and "2, 6" are the leaves.
Box-and-Whisker Plot
A *box-and-whisker plot* (or box plot) is a graphical representation that summarizes the distribution of a dataset by displaying its minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values. It is useful for identifying outliers and understanding the spread and skewness of the data.
**Structure**: The box represents the interquartile range (IQR), which is the range between Q1 (25th percentile) and Q3 (75th percentile). The line inside the box indicates the median (Q2). The "whiskers" extend from the box to the minimum and maximum values within 1.5 times the IQR from Q1 and Q3, respectively. Points outside this range are considered outliers and are often marked with dots.
**How to Read**: The length of the box indicates the variability (spread) of the middle 50% of the data. The position of the median line within the box shows the skewness of the data. The whiskers and any outliers give additional information about the range and spread of the dataset.
**Example**: If a box plot shows a longer whisker on the right and the median closer to Q1, the data is skewed to the right.
Both of these tools are fundamental in business statistics for exploring and presenting data, making it easier to communicate insights about data distributions to stakeholders and decision-makers.
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