Ch 10Descriptive Statistics — Class 11 Applied Mathematics, concept-first.

This concept map shows how the chapter fits together. Descriptive statistics summarises data: its types and handling, its visualisation (bar, pie and line charts, histograms and frequency polygons), i…

Statistics is the science of learning from data — of turning raw numbers into meaningful insight. In this chapter, we focus on descriptive statistics, which is about summarising and presenting data in…

Data is the raw material of statistics, and the first step in any analysis is understanding what kind of data you are holding.

Once we have collected data, the next step is to understand what kind of numbers we are actually holding.

The nominal scale is the most basic level of measurement, where data are simply names or labels with no inherent order or numerical value.

Ordinal data goes a step beyond naming — it tells you the order, but not the distance between positions. Think of class ranks, survey responses like “satisfied” vs.

An interval scale does more than just rank data — it tells you exactly how far apart two measurements are, because the intervals between values are equal and meaningful.

A ratio scale is the most informative level of measurement. It has all the properties of an interval scale — equal intervals between values — but crucially, it also has a true, meaningful zero point.

Data is only as useful as the story it tells. A table of numbers can hide patterns that a simple bar chart or histogram reveals instantly.

A bar graph is a visual tool that uses rectangular bars of equal width to represent and compare different categories of data.

A pie chart is a circular statistical graphic divided into sectors, each representing a proportion of the whole.

A line graph is the natural choice when you want to see how a quantity changes over time — think temperature across a day or sales over months.

A histogram is the natural next step after a frequency distribution — it turns a table of numbers into a picture.

A frequency polygon is a line graph that gives you the same information as a histogram, but in a cleaner, more continuous form.

When we collect data, we end up with a list of numbers that can feel overwhelming. Measures of central tendency give us a single, representative value that sits at the "center" of the data, telling us…

The mean is the most intuitive measure of central tendency — it tells us where the "centre of mass" of the data lies.

The median is the value that splits a dataset into two equal halves when the data is arranged in order.

The mode is the value that appears most frequently in a data set — the observation with the highest count.

Dispersion tells you how spread out the data is — it answers the question: are the values clustered tightly around the centre, or scattered far apart? Averages like the mean or median give you a singl…

The range is the simplest measure of dispersion — it tells you how spread out the data is by looking at the extremes.

Quartile deviation measures the spread of the middle half of your data, ignoring extreme values. It is half the difference between the third quartile () and the first quartile (), giving you a robust…

Mean deviation measures how far, on average, each data point strays from a central value — typically the mean or the median.

Variance measures how far the data points are spread out from their mean — it is the average of the squared deviations.

The standard deviation is the most powerful and widely used measure of spread in statistics. While the range and quartile deviations only look at specific data points, the standard deviation captures…

We have seen how measures of central tendency locate the centre of data and how dispersion tells us about its spread.

Kurtosis tells you how the tails of a distribution behave — whether extreme values are more or less likely than in a normal distribution.

Measures of position tell you where a particular data point sits relative to the rest of the distribution — not just its raw value, but its rank.

Percentile rank answers a natural question: where does a particular score stand relative to the rest of the group? Instead of just knowing your raw mark, you see what percentage of the data lies at or…

Quartile rank is a way of expressing where a particular data point stands relative to the rest of the dataset, using the quartiles as reference points.

When two variables move together — not necessarily because one causes the other, but because their values tend to change in a coordinated way — we say they are correlated.

Statistics is not just a set of formulas — it is a lens for making sense of the world around you. In this section, you will see how the measures you have studied, like the mean, median, and standard d…