Quartiles: Overview, Questions, Preparation

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Statistics Standard Deviation Correlation Bar Graph Chi Square Test Measures of Central Tendency Variance Extrapolation Null Hypothesis Pareto Chart Harmonic Mean How to find Median Statistics Definition Data Collection Methods Frequency Polygons Central Tendency Confidence Interval Data Handling Statistical Inference Quota Sampling Interquartile Range Quartiles Variance and Standard deviation Cluster Analysis Correlation and Regression Graphical Representation Least Square Method Level of Significance Paired T Test Z Score Table Assumed Mean Method Box and Whisker Plot Gamma Distribution Sample Size T Distribution Tests of Significance Types of Statistics Continuous Variable Sample Statistic Exponential Smoothing T Test Table Bivariate Analysis Relative Frequency Difference between Average and ...Difference between Mean and Med...Difference between Parametric a...Grouping data Statistics pdf Mean Absolute Deviation Population and Sample

Rachit Kumar SaxenaManager-Editorial

Updated on Aug 5, 2021 08:31 IST

Table of Contents

What are Quartiles?
Weightage of Quartiles in Class 11
Illustrated Examples on Quartiles
FAQs on Quartiles

What are Quartiles?

Quartiles are the values that split a list into three-quarters of numerical results. The central point of distribution is determined by the middle portion of the three quarters, and the detail near the central point is seen. The lower part of the quarters reveals half of the collection of details below the median, and the upper part shows the other half, which falls above the median. The quartiles represent the data set distribution or dispersion.

Definition:

The whole collection is separated into four equal sections by the quartiles. Thus, the first, second, and third quartiles are represented by Q1, Q2, and Q3, respectively. Q2 is nothing but the median since it reflects the item’s position in the list and is, thus, a positional average. We have to organise the data in ascending order to find quartiles in a set of data.

Formula for Quartiles

Suppose the upper quartile of Q3 is the median of the data set’s upper half. Whereas, Q1 is the lower quartile of the data collection and the median of the lower half. The median is Q2. Remember that we have a variety of objects in a data set. The quartiles are then shown by:

Q1 = [(n+1)/4]th item

Q2 = [(n+1)/2]th item

Q3 = [3(n+1)/4]th item

Weightage of Quartiles in Class 11

In Class 11, you will be taught ‘Quartiles’ in the ‘Statistics’ portion of maths. The weightage is 5-6 marks.

Illustrated Examples on Quartiles

1. Find the quartiles of the following data: 4, 5, 7, 9, 10, 23, 32.
Solution:

Here, n = 7
Lower quartile, Q1 = [(n+1)/4] th item
Q1= 7+1/4 = 2nd item = 5
Median, Q2 = [(n+1)/2]th item
Q2= 7+1/2 item = 4th item = 9
Upper quartile, Q3 = [3(n+1)/4]th item
Q3 = 3(7+1)/4 item = 6th item = 23

2. Find the quartiles for the following data:
23, 13, 37, 16, 26, 35, 26, 35

Solution:
First, arrange the numbers in increasing order.
= 13, 16, 23, 26, 26, 35, 35, 37
The number of items, n = 8.

Lower quartile, Q1 = [(n+1)/4] th item
Q1 = 8+1/4 = 9/4 = 2.25th term
From the quartile formula we can infer:
Q1 = 2nd term + 0.25 (3rd term-2nd term)
Q1= 16+0.25 (23-26) = 15.25.

Similarly,

Median, Q2 = [(n+1)/2]th item
Q2 = 8+1/2 = 9/2 = 4.5
Q2 = 4th term+0.5 (5th term-4th term)
Q2= 26+0.5(26-26) = 26.

Upper quartile, Q3 = [3(n+1)/4]th item
Q3 = 3(8+1)/4 = 6.75th term
Q3 = 6th term + 0.75 (7th term-6th term)
Q3 = 35+0.75 (35-35) = 35

FAQs on Quartiles

Q: What are the four quartiles?

A: The first quartile—representing 25 per cent of the distribution.
The second quartile—representing 50 per cent of the distribution.
The third quartile— representing 75 per cent of the distribution.
The fourth quartile—representing 100 per cent of the distribution.

Q: In statistics, what are quartiles?

A: Quartiles explain how observations are separated into four specified intervals based on data values and how they are compared to the total collection of observations.

Q: How are q1 and q3 calculations performed?

A: Q1 is the median of the lower half of the data (middle), and Q3 is the median of the upper half of the data (middle). Such as (3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Q1 = seven and Q3 = 16.

Q: Are quartiles equal?

A: Quartiles are values that divide a (part of a) table of data into four classes and contain roughly the same number of observations. The 100 per cent total is separated into four equivalent parts: 25 per cent, 50 per cent, 75 per cent, and 100 per cent. The f-value of the third quartile (or upper quartile), Q3, is 0.75.

Q: What is the goal of exploring quartiles?

A: Quartiles are used to summarise a set of numbers. They are also employed for reporting on a collection of data and for making box and whisker graphs.