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- 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
-
For Individual or Ungrouped Data
\[\mathrm{Q}_i=\text{size of }i\left(\frac{n+1}{4}\right)^\text{th Observation.}\quad i=1,2,3\]
-
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
- Quartiles help analyse marks, heights, incomes, and survey results.
- 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]
The following is the distribution of 160 Workers according to the wages in a certain factory:
| Wages more than (in ₹) |
No. of workers |
| 8000 | 160 |
| 9000 | 155 |
| 10000 | 137 |
| 11000 | 91 |
| 12000 | 57 |
| 13000 | 23 |
| 14000 | 10 |
| 15000 | 1 |
| 16000 | 0 |
Determine the values of all quartiles and interpret the results.
For the following data showing weights of 100 employees, find the maximum weight of the lightest 25% of employees.
| Weight (kg) | 45 – 50 | 50 – 55 | 55 – 60 | 60 – 65 | 65 – 70 | 70 – 75 | 75 – 80 |
| No. of employees | 6 | 8 | 15 | 26 | 20 | 14 | 11 |
The following is the frequency distribution of heights of 200 male adults in a factory:
| Height (in cm.) | No. of male adults |
| 145 – 150 | 4 |
| 150 – 155 | 6 |
| 155 – 160 | 25 |
| 160 – 165 | 57 |
| 165 – 170 | 64 |
| 170 – 175 | 30 |
| 175 – 180 | 8 |
| 180 – 185 | 6 |
Find the central height.
Calculate Q3 for the following data.
| Sales (in lakhs ₹) | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |
| No. of firms | 20 | 30 | 70 | 48 | 32 | 50 |
Following is the grouped data for duration of fixed deposits of 100 senior citizens from a certain bank:
| Fixed deposit (in days) | 0 – 180 | 180 – 360 | 360 – 540 | 540 – 720 | 720 – 900 |
| No. of senior citizens | 15 | 20 | 25 | 30 | 10 |
Calculate the limits of fixed deposits of central 50% senior citizens.
