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
Shaalaa.com | Statistics part 2 (Mean Median Mode)
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Related QuestionsVIEW ALL [8]
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 |
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 |
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 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 |
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?
