### Dictionary Rank of a Word | Permutations & Combinations

PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

### Lesson Plan Math Class X (Ch-14) | Statistics

E- LESSON PLAN   SUBJECT MATHEMATICS    CLASS 10

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 Board – CBSE CLASS –X SUBJECT- MATHEMATICS CHAPTER 14  :-  Statistics
TOPIC:-

Chapter 14 Statistics (To find mean, mode, median and frequency ogive)

DURATION:-

This topic is divided into seven modules and are completed in ten class meetings.

PRE- REQUISITE KNOWLEDGE:-

Chapter 14 statistics class 9Th  or mean, mode, median of ungrouped frequency.

TEACHING AIDS:-  Green Board, Chalk,  Duster, Charts  etc.

METHODOLOGY:-  Demonstration and Lecture method

OBJECTIVES:-
• Introduction and method of finding mean of grouped frequency with three methods.
• Method of finding mode of grouped frequency.
• Method of finding median of grouped frequency.
• Method of finding less than and more than ogive.
• Method of finding median from less than type and more than type ogive.
PROCEDURE :-

Start the session by checking their previous knowledge, by asking the questions of mean , mode, median of ungrouped frequency. After this explain the topic to the students.

 S. No. TopicFor Complete Explanation of the topic 1 IntroductionIn this chapter students will learn the method of finding the mean, mode and median of grouped and ungrouped data. Also students will work on the frequency ogive or curve. 2 Calculation of MeanNow teacher will explain different methods of calculating mean with grouped and ungrouped frequency.Mean of ungrouped data$Mean(\overline{X})=\frac{Sum\; of\; all \; observations}{No.\; of\; Observations}$Mean of grouped dataThere are three methods of finding the mean of grouped data (1) Direct method $Mean(\overline{X})=\frac{\sum f_{i}x_{i}}{\sum f_{i}}$ (2) Assumed mean method $Mean(\overline{X})=a+\frac{\sum f_{i}d_{i}}{\sum f_{i}}\\where\: \: d_{i}=x_{i}-a$ (3) Step Deviation method $Mean(\overline{X})=a+\frac{\sum f_{i}u_{i}}{\sum f_{i}}\times h\\ where\: \: u_{i}=\frac{x_{i}-a}{h}$For simple data with less calculation Direct method can be used easily. But for the data with larger terms assumed mean method or step deviation method can be use. 3 Explanation of finding the Missing frequencyNow teacher will explain the method of finding one or two missing frequencies in grouped and ungrouped data. Students should be given sufficient number of problems for practice. 4 Method of finding mode Here teacher will explain  the method of finding the mode with ungrouped data and with grouped data.$Mode = l+\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h$Median Class: Class corresponding to the highest frequency is called Model Class.f1 is the frequency of the model classf0 is the frequency of the class proceeding the median classf2 is the frequency of the class succeeding the median class. 5 Calculation of MedianNow teacher will introduce the topic Median. First of all teacher will explain the Median class and all the abbreviations which are linked with the formula.Median class : A class corresponding to the cumulative frequency ≥ n/2 is called median class.$Median = l+\left (\frac{\frac{n}{2}-C_{f}}{f} \right )\times h$l is the lower limit of median class. Cf is the cumulative frequency of class preceding the median classf is the frequency of median class 6 Ogive: Ogives are of two typesLess than Ogive: This graph can be made by taking upper limits towards the x - axis and cumulative frequency(less than type) towards the y-axis.More than Ogive: This graph can be made by taking lower limits towards the y - axis and cumulative frequency(more than type) towards the y-axis. 7 Finding Median From the Ogive.Here teacher will explain the complete method of finding the median by plotting less than ogive and more than ogive on the same graph paper.Value on the x - axis corresponding to the point of intersection of less then ogive and more than ogive is called the median .Teacher will also explain the method of finding the median for single curve.In a single curve, Median is the value on the x-axis corresponding to the value = n/2 on the y-axis.

EXPECTED OUTCOMES:-
• After studying this lesson students should know
• All formulas of finding mean of the given data.
• All formulas of finding mode of the given data.
• All formulas of finding median of the given data.
• Method of finding the less than ogive and more than ogive and the median from the graph.
• The relation between mean, mode median (Empirical formula)
• Students should also know the method of implementation of these formulas in simple and complex problems.
STUDENTS DELIVERABLE:-
• Review questions given by the teacher.
• Students should prepare the presentation on the basic concepts and formulas on statistics.
• Solve NCERT problems with examples.
• solve assignment given by the teacher.
EXTENDED LEARNING:-

Students can extend their learning through the RESOURCE CENTRE and can find more valuable and interesting concepts on mathematics at  cbsemathematics.com

ASSESSMENT TECHNIQUES:-
Assignment sheet will be given as home work at the end of the topic. Separate sheets which will include questions of logical thinking and Higher order thinking skills will be given to the above average students.
Class Test , Oral Test , worksheet and Assignments can be made the part of assessment.
Re-test(s) will be conducted on the basis of the performance of the students in the test.

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