What went wrong when the king rode under the arch?

It was too low and knocked off his crown

How does the chain of blame unfold in the poem?

Each accused person blames another, ending with the king's own changes

What is classification of data and why is it needed?

Classification arranges raw data into groups or classes by some criterion; it brings order to disorganised data and makes comparison, location and statistical analysis easier.

Distinguish between chronological and spatial classification.

Chronological classification arranges data by time, such as population by years (a time series), while spatial classification arranges data by geographical location, such as the yield of wheat across countries.

Distinguish between a continuous and a discrete variable.

A continuous variable can take any value including fractions within a range, like height; a discrete variable changes only by finite jumps and takes only certain values, like the number of students.

Define class limits, class interval and class mark.

The class limits are the two ends of a class (lower and upper); the class interval is their difference; the class mark is their mid-value, \((\text{Upper limit}+\text{Lower limit})/2\).

Distinguish between the inclusive and exclusive methods.

In the inclusive method both class limits are counted within the class, while in the exclusive method an item equal to a class limit is placed in the next class so one limit is excluded.

Why is an adjustment made in class intervals for continuous data?

When inclusive classes leave a gap between the upper limit of one class and the lower limit of the next, half the gap is subtracted from lower limits and added to upper limits to restore continuity.

Explain loss of information in classified data.

When data are grouped, individual observations lose significance because every value in a class is treated as equal to the class mark, so the actual values are no longer used in calculations.

What is a frequency array?

The classification of a discrete variable in which the frequency is shown against each integral value of the variable, such as the number of households of each size.

What is a bivariate frequency distribution?

A table showing the joint frequency distribution of two variables, with one variable in columns and the other in rows and each cell showing the corresponding frequency.

Organisation of Data

Q: What is a frequency distribution?

A comprehensive table that shows how the different values of a quantitative variable are distributed across classes along with their corresponding class frequencies.

Class 11 Economics · Statistics for Economics · Chapter 3

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Summary

Once data are collected they are raw and disorganised, so the next step is to classify them to bring order and make further analysis possible. Classification means arranging data into groups or classes on the basis of some criterion. Data may be classified chronologically (by time, such as years — a time series), spatially (by place), qualitatively (by an attribute like gender or literacy that cannot be measured) or quantitatively (by a measurable characteristic like income). Variables are of two types: a continuous variable, like height, can take any value including fractions within a range, while a discrete variable, like the number of students, changes only by finite jumps. A frequency distribution shows how the values of a quantitative variable are distributed across classes with their frequencies. Each class has a lower and an upper limit; the class interval is their difference and the class mark or mid-point their average, \((\text{Upper limit}+\text{Lower limit})/2\). Classes may be formed by the inclusive method (both limits counted) or the exclusive method (one limit excluded and placed in the next class); for continuous data an adjustment restores continuity between gaps. Frequencies are counted using tally marks. Classifying data causes a loss of information, because individual observations are replaced by the class mark in later calculations. A discrete variable's data are shown as a frequency array, while the joint distribution of two variables forms a bivariate frequency distribution.

Organisation of Data

Key terms

Classification

Arranging raw data into groups or classes on the basis of some common criterion.

Continuous variable

A variable that can take any value, including fractions, within a range, such as height or weight.

Discrete variable

A variable that changes only by finite jumps and takes only certain values, such as the number of students.

Frequency distribution

A table showing how the values of a variable are distributed across classes with their frequencies.

Class mark

The mid-value of a class, equal to the average of its upper and lower class limits.

Bivariate frequency distribution

A table showing the joint frequency distribution of two variables together.

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Classification of data means:

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Organisation of Data

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