Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

What is the deivation of the formulae for finding median and mode of grouped data? (as listed in class 10 mathematics book)
Asked by reetatyagi8 | 06 Aug, 2015, 10:08: AM
answered-by-expert Expert Answer
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
C o n s i d e r space t a k i n g space c l a s s space i n t e r v a l s space a l o n g space x minus a x i s space a n d space c u m u l a t i v e space f r e q u e n c e space a l o n g space y minus a x i s a n d space d r a w space a n space o g i v e space c u r v e space a s space a b o v e. W e space k n o w space t h a t space M e d i a n equals open parentheses N over 2 close parentheses to the power of t h end exponent space t e r m F equals c u m u l a t i v e space f r e q u e n c y space o f space t h e space c l a s s space p r e c e d i n g space t h e space m e d i a n space c l a s s. f equals f r e q u e n c y space o f space t h e space m e d i a n space c l a s s h equals c l a s s space w i d t h L subscript m equals L o w e r space l i m i t space o f space t h e space m e d i a n space c l a s s O g i v e space i s space a space c u r v e space a n d space w e space a r e space a s s u m i n g space t h a t space d a t a space a r e space u n i f o r m l y space d i s t r i b u t e d space w i t h i n space t h e space m e d i a n space c l a s s. A n d space w e space a r e space t r y i n g space t o space f i t space t h e space d a t a space i n space a space s t r a i g h t space l i n e. T h u s space w e space a r e space a p p r o x i m a t i n g space t h e space c u r v e space A S R D space a s space t h e space s t r a i g h t space l i n e space A C D. T h i s space m e t h o d space o f space f i t t i n g space t h e space d a t a space u sin g space l i n e a r space p o l y n o m i a l s space i s space c a l l e d space c u r v e space f i t t i n g comma space a space m e t h o d space o f space l i n e a r space i n t e r p o l a t i o n. T h r o u g h space N over 2 comma space d r a w space a space s t r a i g h t space l i n e space t o space m e e t space t h e space c u r v e space a t space S. N o w space c o n s i e r space t h e space t r i a n g l e s space A B C space a n d space A E D. W E space n e e d space t o space f i n d space x subscript 0. H e r e comma space angle B A C equals angle E A D angle A B C equals angle A E D equals 90 degree T h u s comma space b y space A A space s i m i l a r i t y comma space w e space h a v e comma triangle A B C tilde triangle A E D H e n c e space t h e space s i d e s space o f space t h e space t r i a n g l e space a r e space p r o p o r t i o n a l. rightwards double arrow fraction numerator A B over denominator U V end fraction equals fraction numerator B C over denominator D E end fraction rightwards double arrow fraction numerator space x subscript 0 over denominator h end fraction equals fraction numerator begin display style N over 2 end style minus F over denominator f end fraction rightwards double arrow space x subscript 0 equals open square brackets fraction numerator begin display style N over 2 minus F end style over denominator f end fraction close square brackets cross times h T h e r e f o r e comma space M e d i a n equals L subscript m plus x subscript 0 equals L subscript m plus open square brackets fraction numerator begin display style N over 2 minus F end style over denominator f end fraction close square brackets cross times h
Answered by Vimala Ramamurthy | 06 Aug, 2015, 12:35: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
mode-median = ________
Asked by tanya78904321 | 24 Sep, 2023, 07:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
if the mode and median are 9.2 and 9...find mean  
Asked by lisajameson338 | 25 Jan, 2023, 09:03: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find the median of 256308497
Asked by bushrafatima6892 | 20 Apr, 2022, 04:02: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find the mean of 20 numbers such that if the mean of 8 of them is 10 and the mean of 10 of them is 12 the last two numbers are 8 and 12
Asked by amulya2194 | 17 Apr, 2022, 04:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
how to draw table
Asked by pawarsachin | 16 Dec, 2021, 07:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
what is mean grouped data formula
Asked by palivelamanikyalarao123 | 10 Oct, 2021, 12:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
9.If the mean of the following data is 91.Find the missing frequency :- C. I.            Frequency 0-30.             12 30-60.           21 60-90.            X  90-120.         52 120-150.        Y  150-180.        11 Total              150
Asked by prajapatisohil573 | 02 Aug, 2021, 10:03: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
RELATIONSHIP BETWEEN MEAN MEADIAN AND MODE??
Asked by nandinisingh030206 | 25 Mar, 2021, 03:33: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
by assume mean method
question image
Asked by 8416mayankkumar | 14 Mar, 2021, 07:35: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Statistics
Asked by Tesbthmarak | 05 Mar, 2021, 09:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×