STATISTICS
Frequently Asked Questions
Statistics is the branch of mathematics that deals with the collection, organisation, presentation, analysis, and interpretation of numerical data.
Statistics helps in understanding trends, making comparisons, predicting outcomes, and taking data-based decisions in real-life situations.
Data refers to numerical information collected from observations, surveys, or experiments for analysis.
Raw data is unorganised data collected directly from a source without any classification or arrangement.
Grouped data is data organised into class intervals to simplify analysis when observations are large in number.
It is a table that shows how often values occur within defined class intervals.
Class intervals are divisions of data into fixed ranges used to group observations.
Class width is the difference between the upper and lower limits of a class interval.
The class mark is the midpoint of a class interval, calculated as \((\text{upper limit} + \text{lower limit})/2\).
Measures of central tendency describe a central or typical value of data, such as mean, median, and mode.
Mean is the average value of grouped data calculated using class marks and frequencies.
\(\bar{x} = \frac{\sum f_i x_i}{\sum f_i}\), where \(x_i\) are class marks and \(f_i\) are frequencies.
It is a method to calculate mean by assuming a convenient value as the mean to simplify calculations.
A short-cut method of finding mean using deviations divided by class width to reduce computation.
It is preferred when class intervals are equal and numbers are large.
Median is the value that divides the data into two equal parts when arranged in order.
The class interval that contains the median value.
\(\text{Median} = l + \left(\frac{\frac{N}{2} - cf}{f}\right)h\)
\(l\): lower limit, \(N\): total frequency, \(cf\): cumulative frequency before median class, \(f\): frequency, \(h\): class width
Mode is the value that occurs most frequently in a data set.
The class interval with the highest frequency.
\(\text{Mode} = l + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right)h\)
\(f_1\) is modal class frequency, \(f_0\) preceding frequency, \(f_2\) succeeding frequency.
It is the running total of frequencies in a distribution.
A graphical representation of cumulative frequencies, also called an ogive.
An ogive formed using cumulative frequencies less than the upper class limits.
An ogive drawn using cumulative frequencies greater than the lower class limits.
By plotting both ogives and locating the x-coordinate of their intersection.
They summarise large data sets using a single representative value.
Mean is best for symmetrical distributions.
Median is preferred for skewed distributions.
When identifying the most common value, such as shoe size or popular choice.
Economics, science, medicine, education, population studies, and business analysis.
To analyse results, performance trends, and assessment outcomes.
Numerical problems, formula-based questions, graphical interpretation, and case-study questions.
Errors in tables lead to incorrect calculations and wrong conclusions.
Wrong class marks, incorrect cumulative frequencies, and formula substitution errors.
All major steps with formulas must be clearly shown for full marks.
Yes, for a perfectly symmetrical distribution.
Changing the origin and scale using assumed mean and step deviation.
Drawing conclusions and inferences from analysed data.
Analytical thinking, logical reasoning, and numerical accuracy.
Yes, due to formula-based questions and structured solutions.
Memorise formulas, practice numericals, and avoid calculation mistakes.
It carries significant weightage in the Class X Mathematics examination.
Proper scale, labeling, and accuracy are essential for full marks.
Frequency per unit class width, used in unequal class intervals.
Yes, they help compare distributions visually.
Displaying data using tables, graphs, and curves.
It teaches how data can be analysed logically to draw meaningful conclusions.
