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Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14 PDF

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Statistics CBSE NCERT Notes Class 10 Maths Chapter 14 PDF

Arithmetic Mean (AM)

Arithmetic Mean of Unclassified Data

If n numbers be x1, x2, x3, …, xn, then the arithmetic mean of these unclassified data is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Arithmetic Mean of Frequency Distribution

If f1, f2, f3, …, fn, be the frequency of n numbers x1, x2, x3, …, xn, then the arithmetic mean of these frequency distribution is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Arithmetic Mean of Class Interval Data

To find the mean of a classified data, we first find class marks x1, x2, x3, …, xn, of the class intervals as the variables and take the frequencies of the classes f1, f2, f3, …, fn, as the corresponding frequencies of the variables. Then, the arithmetic mean of these classified data is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Deviation of a Term

The deviation of a term from the arithmetic mean is the quantity by which that term exceeds the arithmetic mean. If the variable be x and AM be A, then AM (x – A) is the deviation of x from A. Thus, the deviation is d = x – A.

Assumed Mean Method of AM for Simple Distribution

The arithmetic mean of n simple distribution when the assumed mean (a) and deviation d = x – A is given is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Assumed Mean Method of AM for Frequency Distribution

The arithmetic mean of  frequency distribution when the assumed mean (a) and deviation d = x – A is given is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Step Deviation Method for AM

The step deviation method for arithmetic mean is where ‘a’ is assumed mean and u = (xi – A)/h 

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Class 10 Maths Chapter 14 Examples 1:

Find the mean by assumed mean method. 

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

First, make a frequency distribution table as below with assumed mean and deviations.

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Using assumed mean method, we get

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Median

Median of Unclassified Data

First, we arrange the terms in ascending or descending order and then find the number of terms.

If ‘n’ is odd, then the median is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

If ‘n’ is even, then the median is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Median of Classified Data

If in a continuous distribution the total frequency be N then the class whose commutative frequency is either equal to N/2 of just greater than N/2 is called the median class

The median of continuous distribution is 

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

where

l = Lower limit of median class

f = Frequency of median class

N = Total Frequency

CF = Cumulative Frequency of class just before median class 

h = Class size of median class

Class 10 Maths Chapter 14 Examples 2:

Find the median.

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

First, cumulative frequency is made as in table below. 

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Using Median formula, we get

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Mode

Mode of Unclassified Data

In unclassified distribution, the mode is the data with highest frequency.

Mode of Classified Data

In unclassified distribution, the mode is the data with highest frequency.

The class with highest frequency is the mode class.

The mode of continuous distribution is

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

where

l = Lower limit of mode class

f = Frequency of mode class

f-1 = Frequency of pre-mode class

f-1 = Frequency of post-mode class

h = Class size of mode class

Class 10 Maths Chapter 14 Examples 3:

Find the mode. 

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Using the formula, we get

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Empirical Relations

Relation Among Mean, Median & Mode

The relation between mean, median and mode is Mode = 3Median – 2Mean.

Ogive Curve

Graphical Representation of Cumulative Frequency.

Ogive curve is a graph that is used to find the median graphically.

To represent the graph of cumulative frequency curve, you need find LESS THAN and MORE THAN cumulative points and then plot it on coordinate axes.

For better understand, start with an example.

Class 10 Maths Chapter 14 Examples 4:

Draw an ogive curve and then find the median.

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

First, you need to find cumulative frequency of the above data.

Statistics CBSE NCERT Notes Class 10 Maths Chapter 14 PDF

For LESS THAN Ogive Curve, you need to select Upper Limit of each class as x-coordinate and LESS THAN cumulative frequency of corresponding class as y-coordinate.

It means, plot (10, 2), (15, 14), (20, 16), (25, 20), (30, 23), (35, 27), (40, 30) for LESS THAN Ogive curve.

For MORE THAN Ogive Curve, you need to select Lower Limit of each class as x-coordinate and MORE THAN cumulative frequency of corresponding class as y-coordinate.

It means, plot (5, 30), (10, 28), (15, 16), (20, 14), (25, 10), (30, 7) and (35, 3). for MORE THAN Ogive curve.

The intersection point of LESS THAN and MORE THAN Ogive curve gives the value of median on x-axis. Thus, the median of the given data is 17.5.

Statistics Mean Median Mode CBSE Notes Class 10 Maths Chapter 14

Click below to get CBSE Class 10 Maths Chapter wise Revision Notes PDF.

Chapter NoChapter name
Chapter 1 :Real Numbers CBSE Class 10 Maths Revision Notes
Chapter 2 :Polynomials CBSE Class 10 Maths Revision Notes
Chapter 3 :Pair of Linear Equations in Two Variables CBSE Class 10 Maths Revision Notes
Chapter 4 :Quadratic Equations CBSE Class 10 Maths Revision Notes
Chapter 5 :Arithmetic Progression CBSE Class 10 Maths Revision Notes
Chapter 6 :Triangles CBSE Class 10 Maths Revision Notes
Chapter 7 :Coordinate Geometry CBSE Class 10 Maths Revision Notes
Chapter 8 :Introduction to Trigonometry CBSE Class 10 Maths Revision Notes
Chapter 9 :Some Applications of Trigonometry CBSE Class 10 Maths Revision Notes
Chapter 10 :Circles CBSE Class 10 Maths Revision Notes
Chapter 11 :Constructions CBSE Class 10 Maths Revision Notes
Chapter 12 :Area Related to Circles CBSE Class 10 Maths Revision Notes
Chapter 13 :Surface Areas & Volumes CBSE Class 10 Maths Revision Notes
Chapter 14 :Statistics CBSE Class 10 Maths Revision Notes
Chapter 15 :Probability CBSE Class 10 Maths Revision Notes

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