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CBSEArts (English Medium) Class 11
Textbook Solutions12668
Concept Notes & Videos337
Syllabus

Quartiles

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Topics

  • Introduction
  • Calculation
  •  Application
  • Real-Life Application
  • Key Point Summary
Maharashtra State Board: Class 11

Introduction

  • Quartiles are values that divide a dataset (when arranged in order) into four equal parts.
  • There are three quartiles:
    First Quartile (Q1): 25% of the data lies below Q1.
    Second Quartile (Q2): 50% below this value; this is the Median.
    Third Quartile (Q3): 75% below this value; it marks the upper quarter. 
Maharashtra State Board: Class 11

Calculation

  1. For Individual or Ungrouped Data 
    \[\mathrm{Q}_i=\text{size of }i\left(\frac{n+1}{4}\right)^\text{th Observation.}\quad i=1,2,3\]

  1. For Grouped/Continuous Data 
    \[\mathbf{Q}_i=l+\left(\frac{\frac{in}{4}-cf}{f}\right)\times h\quad i=1,2,3\]
    Where 
    l = Lower limit of quartile class.
    f = Frequency of the quartile class
    cf = Cumulative frequency of the class preceding the quartile class.
    n = Total of frequency.
    h = Upper limit - lower limit of the quartile class. 

Maharashtra State Board: Class 11

Application

  1. Quartiles help analyse marks, heights, incomes, and survey results.
  2. Useful for understanding income groups, data spread, and outlier detection.
Maharashtra State Board: Class 11

Real-Life Application

Quartiles are like slicing a pizza into four equal pieces. Each 25% portion is separated by a quartile cut!

Maharashtra State Board: Class 11

Key Point Summary

  • Quartiles split data into four sections.
  • Q2 is always the median of the dataset.
  • Quartiles are practical tools for comparing groups and finding outliers.

Test Yourself

Related QuestionsVIEW ALL [15]

Monthly consumption of electricity (in units) of families in a certain locality is given below:

205, 201, 190, 188, 194, 172, 210, 225, 215, 232, 260, 230.

Calculate electricity consumption (in units) below which 25% of families lie.

Answer the following questions on the basis of the given data :

Marks 10 20 30 40 50
No. of Students 4 7 13 8 6

1) Write the formula of Q1 and Q3.

2) Find out the median of the above data?

3) Find out the cumulative frequency of the last value in the above data.

4) Find out the value of 'n' in the above data

Compute all the quartiles for the following series of observations:
16, 14.9, 11.5, 11.8, 11.1, 14.5, 14, 12, 10.9, 10.7, 10.6, 10.5, 13.5, 13, 12.6.

The heights (in cm) of 10 students are given below: 148, 171, 158, 151, 154, 159, 152, 163, 171, 145. Calculate Q1 and Q3 for above data.

Give economic term:

Value that divides the whole set of observations into four equal parts.

For the following data of daily expenditure of families (in ₹), compute the expenditure below which 75% of families include their expenditure.

Daily expenditure (in ₹) 350 450 550 650 750
No. of families 16 19 24 28 13

Give the correct option:

Statements that do not apply to Quartiles.

  1. First, arrange the values in ascending or descending order.
  2. Observation can be divided into 4 parts.
  3. They are represented as Q1, Q2 and Q3.
  4. Q2 is also known as a median.
Weight (kg) 40 – 45 45 – 50 50 – 55 55 – 60 60 – 65 65 –70 70 – 75 75 – 80
No. of person 4 15 20 30 20 10 8 4

For above data, find all quartiles and number of persons weighing between 57 kg and 72.

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