12th Standard Geography — Statistical Techniques Online Test

About Statistical Techniques

Medium ~60 min study

Statistical Techniques is the thirteenth unit of the Tamil Nadu State Board Class 12 Geography book and the last unit of Practical Geography. It defines statistics as a branch of science which deals with quantitative data, through four processes: collection, presentation, analysis and interpretation of data.

The lesson explains why geographers need statistics, separates qualitative from quantitative data and primary from secondary data, and shows how raw data is organised into a frequency distribution. It then works through the three averages, mean, median and mode, for both individual values and grouped data, using examples from Cuddalore, Chennai and Cochin.

This page has additional one mark questions built from the lesson, including short sums on range, midpoint, mean, median and mode. The book exercise has only three numerical problems and no printed multiple choice questions, so every question here is checked against the lesson text and its worked examples.

What you'll learn

• Explain the four processes of statistics and why geographers use statistics.
• Distinguish qualitative, quantitative, primary and secondary data.
• List the methods of primary and secondary data collection.
• Find the range, midpoint and class interval and use tally marks.
• Calculate the mean, median and mode of individual and grouped data.
• Identify the median class and the modal class of a frequency distribution.

Before you start

• Simple addition, division and averages from school mathematics.
• Reading a table of values such as monthly temperature or rainfall.
• Earlier Practical Geography units on representing geographical data.

Statistical Techniques explained

What this lesson covers

Role of statistics in geography

Wherever data are collected and summarised or numerical information is analysed, statistics is needed for sound analysis. Geographers use it to describe spatial data, generalise complex spatial patterns, estimate the probability of outcomes at a location, infer a population from samples, compare places and test an actual pattern against an expected one.

Types and collection of data

Qualitative data only describes an item; quantitative data has a numerical value. Primary data is collected by the investigator from door to door through direct personal investigation, indirect oral investigation or a questionnaire. Secondary data comes from published or unpublished sources.

Organisation of data

Range is the highest value minus the lowest value. An array arranges raw data in ascending or descending order, and a frequency distribution arranges it into classes. Its terms are class, class limit, midpoint, class interval, tally marks, class frequency and total frequency.

Measures of central tendency

An average is one figure that represents the whole data, so it lies between the extremes. Mean is the sum of values divided by their number; for grouped data it uses an assumed mean. Median is the middle value and divides the series into two equal parts. Mode is the most frequent value; for grouped data it is found from the modal class.

Common mistakes to avoid

• Calling the language spoken quantitative data. It only describes an item, so it is qualitative.
• Treating published sources as a primary method. They are a method of secondary data collection.
• Taking the 6th item as the median of 12 items. The median is the 6.5th item, the average of the 6th and 7th.
• Using the cumulative frequency of the median class itself for m. m is the cumulative frequency of the class preceding the median class.
• Mixing up f0 and f2 in the mode formula. f0 precedes the modal class and f2 succeeds it.

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

What is statistics according to the 12th Geography book?

Statistics is a branch of science which deals with quantitative data. It includes four processes: collection of data, presentation of data, analysis of data and interpretation of data. Wherever data are collected, summarised or analysed, statistics is needed for sound analysis and interpretation of results.

What is the difference between primary and secondary data?

Primary data are the statistical materials which the investigator collects by going from door to door for his or her study, through direct personal investigation, indirect oral investigation or a questionnaire. Secondary data are already collected and recorded data taken from published or unpublished sources.

How is the range of data found?

Range is the difference between the highest and lowest values in the data. For 2, 6, 4, 9, 12, 8, 5, 8 the highest value is 12 and the lowest is 2, so the range is 12 - 2 = 10.

What are tally marks?

Tally marks are vertical bars put for every observation while counting frequencies. They come in groups of five: after four bars a cross stroke is put for the fifth observation, which makes counting the frequency of each class easy.

How is the mean of grouped data calculated?

The book uses the assumed mean method: mean = A + (sum of fd / N) x i, where d = (x - A)/i. For the plant heights example, A = 25, sum of fd = 50, N = 50 and i = 10, so the mean is 25 + 10 = 35.

How is the median of twelve values found?

Arrange the values in ascending order and take the (N+1)/2 th item. For 12 values this is the 6.5th item, the average of the 6th and 7th items. For Chennai's minimum temperatures it is (24.6 + 25.6)/2 = 25.1.

How is the mode of grouped data calculated?

First find the modal class, the class with the maximum frequency. Then mode = l + (f1 - f0)/(2f1 - f0 - f2) x c. For daily wages with modal class 50 - 60, f1 = 15, f0 = 12, f2 = 12 and c = 10, the mode is 50 + 5 = 55.