Topics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Commercial Mathematics
Goods and Services Tax (G.S.T.)
Banking
Algebra
Geometry
Shares and Dividends
Symmetry
Mensuration
Linear Inequations
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Trigonometry
Statistics
Problems on Quadratic Equations
- Method for Solving a Quadratic Word Problem
- Problems Based on Numbers
- Problems on Ages
- Problems Based on Time and Work
- Problems Based on Distance, Speed and Time
- Problems Based on Geometrical Figures
- Problems on Mensuration
- Problems on C.P. and S.P.
- Miscellaneous Problems
Ratio and Proportion
Probability
Remainder Theorem and Factor Theorem
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic Progression
Geometric Progression
Reflection
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Section and Mid-Point Formulae
Equation of a Line
Similarity
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Angle and Cyclic Properties of a Circle
Tangent Properties of Circles
Constructions
Volume and Surface Area of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Graphical Representation of Statistical Data
Measures of Central Tendency (Mean, Median, Quartiles and Mode)
Probability
- Definition: Median
- Formula: Odd Number of Observations
- Formula: Even Number of Observations
- Example 1
- Example 2
- Example 3
- Key Points Summary
Definition: Median
Median is the value of the middle-most observation(s). The median is a measure of central tendency which gives the value of the middle-most observation in the data.
Formula: Odd Number of Observations
If the number of data points (n) is odd, the median is,
Median = `((n+1)/2)^(th)` term
Formula: Even Number of Observations
If n is even, the median is the average of the values at positions
Median = Average of `(n/2)^(th)` and `(n/2+1)^(th)` values
Example 1
Question: Find the median of:
(i) 9, 7, 6, 14, 10, 4 and 11; (ii) 2, 5, 9, 4, 12, 3, 7, 4, 10 and 7.
Solution:
(i) 9, 7, 6, 14, 10, 4 and 11;
Steps
-
Arranged in ascending order.
4 6 7 9 10 11 14 -
The middle term(s) are directly identified by counting.
4 6 7 9 10 11 14
Clearly, middle term is 9; therefore, the median = 9
(ii) 2, 5, 9, 4, 12, 3, 7, 4, 10 and 7
Steps
-
Arranged in ascending order.
2 3 4 4 5 7 7 9 10 12 -
The middle term(s) are directly identified by counting.
2 3 4 4 5 7 7 9 10 12 - Number of data = 10, which is even
The average of two middle values (for even)|
⇒ The two middle data = 5 and 7
∴ Median = Average of 5 and 7 = `"5 + 7"/"2"` = 6
Example 2
Question: The following are scores obtained by 11 players in a cricket match 7, 21, 45, 12, 56, 35, 25, 0, 58, 66, 29. Find the median score.
Solution:
Let us arrange the values in ascending order.
0,7,12,21,25,29,35,45,56,58,66
The number of values = 11 which is odd
Median = `((n+1)/2)^(th)` term
Median = `((11+1)/2)^(th)` value
= `(12/2)^(th)` value = 6th value = 29
Example 3
Example 8.9 For the following ungrouped data: 10, 17, 16, 21, 13, 18, 12, 10, 19, 22. Find the median.
Solution:
Arrange the values in ascending order.
10, 10, 12, 13, 16, 17, 18, 19, 21, 22.
The number of values = 10
Median = Average of `(n/2)^(th)` and `(n/2+1)^(th)` values
Median = Average of `(10/2)^(th)` and `(10/2+1)^(th)` values
= Average of 5th and 6th values
= `(16 + 17)/2 = 33/2 = 16.5`
Key Points Summary
Definition: The middle value in an ordered set of data.
Essential Rule: Always sort the data (ascending or descending) first.
Outlier Resistant: The median is not affected by extreme values (outliers), unlike the mean.
Odd vs. Even:
- Odd (n): The median is the single middle data point.
- Even (n): The median is the average of the two middle data points.
Example Question 1
Find the median of the data: 24, 36, 46, 17, 18, 25, 35
We arrange the data in ascending order, we get 17, 18, 24, 25, 35, 36, 46 Median is the middle observation.
Therefore 25 is the median.
Test Yourself
Video Tutorials
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Related QuestionsVIEW ALL [8]
Ten students appeared for a test in Mathematics and Statistics and they obtained the marks as follows:
| Sr. No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Marks in Mathematics | 42 | 38 | 36 | 32 | 23 | 25 | 35 | 37 | 25 | 23 |
| Marks in Statistics | 22 | 26 | 29 | 34 | 50 | 45 | 23 | 28 | 32 | 36 |
If the median will be the criteria, in which subject, the level of knowledge of the students is higher?
The following is the data of pocket expenditure per week of 50 students in a class. It is known that the median of the distribution is ₹120. Find the missing frequencies.
| Expenditure per week (in ₹) |
0 – 50 | 50 – 100 | 100 – 150 | 150 –200 | 200 –250 |
| No. of students | 7 | ? | 15 | ? | 3 |
From the following distribution, determine median graphically.
| Daily wages (in ₹) | No. of employees |
| Above 300 | 520 |
| Above 400 | 470 |
| Above 500 | 399 |
| Above 600 | 210 |
| Above 700 | 105 |
| Above 800 | 45 |
| Above 900 | 7 |
The median of the following incomplete table is 92. Find the missing frequencies:
| C.I. | 30 – 50 | 50 – 70 | 70 – 90 | 90 – 110 | 110 – 130 | 130 – 150 | Total |
| f | 6 | ? | 18 | 20 | ? | 10 | 80 |
Find the missing frequency given that the median of the distribution is 1504.
| Life in hours | No. of bulbs |
| 950 – 1150 | 20 |
| 1150 – 1350 | 43 |
| 1350 – 1550 | 100 |
| 1550 – 1750 | - |
| 1750 – 1950 | 23 |
| 1950 – 2150 | 13 |
