Q.Explain the findings of the boxplot of Figure 4.18 by filling the following blanks:

Boxplot Interpretation – A First Look

Imagine you and your friends are comparing how much pocket money you each get in a month. Some get very little, some get a moderate amount, and a few get a lot. If you wanted to show this information in a single picture — without listing every single amount — you could use a boxplot. It’s a simple diagram that tells you, at a glance, where most people lie, how spread out the amounts are, and whether anyone is unusually high or low.

What a Boxplot Actually Shows

A boxplot (also called a box-and-whisker plot) is built from five key numbers that summarise a set of data. These numbers are called the five-number summary. The NCERT textbook for Class 11 (Statistics) introduces this concept in the chapter on Graphical Representation of Data. The five numbers are:

• The minimum value (the smallest observation)
• The first quartile (Q1) – the value below which 25% of the data lies
• The median (Q2) – the middle value, splitting the data into two halves
• The third quartile (Q3) – the value below which 75% of the data lies
• The maximum value (the largest observation)

The box itself runs from Q1 to Q3. This box contains the middle 50% of the data — the most typical range. A line inside the box marks the median. Two lines (whiskers) extend from the box to the minimum and maximum values, unless there are outliers (unusually extreme values), which are shown as separate dots.

How to Read a Boxplot – Step by Step

When you see a boxplot, ask yourself these questions in order:

1. Where is the median? If the median line is closer to the bottom of the box, the lower half of the data is more spread out; if it’s near the top, the upper half is more spread out. If it’s in the middle, the data is fairly symmetric.

2. How long is the box? A long box means the middle 50% of values are spread far apart — high variability. A short box means most values are clustered close together.

3. How long are the whiskers? Long whiskers indicate that the data extends far from the middle. Short whiskers mean the data is tightly packed.

4. Are there any dots beyond the whiskers? Those are outliers — values that are unusually far from the rest. They might be errors, or they might be genuinely exceptional cases worth investigating.

Why Boxplots Matter in Commerce/Humanities

You won’t be asked to draw a boxplot or calculate quartiles in a prose exam. But you will be asked to interpret one. Here’s why it’s useful:

• Comparing groups: In economics, you might compare income distributions across states. A boxplot shows which state has a higher median income, which has greater inequality (longer box), and which has extreme rich or poor outliers.
• Spotting skewness: If the median is not in the middle of the box, the data is skewed. For example, in a boxplot of household savings, a median near the bottom of the box suggests that most people save little, while a few save a lot (right-skewed). …