Statistics For Class X

Covers All The Topics Needed For A Class X Student
By :- Somil Jain

1. E.c.s . bagless school

2. List of Group Members Somil Jain Shivangi Kushwah Anshul Rajput Rishi Rajput Shikha Agrawal Ankit Sharma Kashfi Khan

3. Maths Project Work Maths F.A. activity

4.  "There are three kinds of lies: lies, damned lies and statistics." — by Benjamin Disraeli Statistics

5. Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with astatistical population or a statistical model process to be studied .  Introduction

6. Measure Of Central Tendency The Study Of Certain Numerical Representatives of the ungrouped data is called measures of central tendency There are three measures of central tendency Mean Median Mode

7. Mean The Mean Is The Average Of The Numbers: A Calculated "Central" Value Of A Set Of Numbers. There Are Three Methods To Calculate Out Mean And These Are:-

8. In Which :- a = assumed mean d = x - a In Which :- a = assumed mean h = class size u = x - a h

9. Mode The "Mode" Is The Value That Occurs Most Often. If No Number Is Repeated, Then There Is No Mode For The List. For Ungrouped Data The Observation Which Occurs Maximum Number Of Time

10. For Grouped Data Where :- l = lower limit of mode class h = class size F 1 = frequency of mode class F = frequency of the class just before modal class F 2 = frequency of the class successding the modal class

11. Median The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. For Ungrouped Data If No. Of Observations , n = Odd

12. If No. Of Observations , n = Even For grouped data Where :- l = Lower limit of median class n = Number of observations CF = Cumulative frequency of previous Class just before median class F = Frequency of median class h = Class size

13. Relation Among Mean, Median & Mode 3 Median = Mode + 2Mean

14. Also known as an OGIVE , this is a curve drawn by plotting the value of the first class on a graph. The next plot is the sum of the first and second values, the third plot is the sum of the first, second, and third values, and so on. Cumulative Frequency Curve

15. Example:- During the medical check-up of 35 students of a class, their weights were recorded as follows: Weight (in kg) Number of students Less than 38 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Draw a less than type ogive for the given data. Hence obtain the median weight from the graph verify the result by using the formula.

16. Weight (in kg) upper class limits Number of students (cumulative frequency) Less than 38 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Solution:- The given cumulative frequency distributions of less than type are Taking upper class limits on  x -axis and their respective cumulative frequencies on  y -axis, its ogive can be drawn as follows.

17. Here,  n  = 35 So,   = 17.5 Mark the point A whose ordinate is 17.5 and its  x -coordinate is 46.5. Therefore, median of this data is 46.5.

18. It can be observed that the difference between two consecutive upper class limits is 2. The class marks with their respective frequencies are obtained as below.

19. Weight (in kg) Frequency (f) Cumulative frequency Less than 38 38 − 40 3 − 0 = 3 3 40 − 42 5 − 3 = 2 5 42 − 44 9 − 5 = 4 9 44 − 46 14 − 9 = 5 14 46 − 48 28 − 14 = 14 28 48 − 50 32 − 28 = 4 32 50 − 52 35 − 32 = 3 35 Total (n) 35 The cumulative frequency just greater than i s 28, belonging to class interval 46 − 48. Median class = 46 − 48 Lower class limit ( l ) of median class = 46

20. Frequency ( f ) of median class = 14 Cumulative frequency ( cf ) of class preceding median class = 14 Class size ( h ) = 2 Therefore, median of this data is 46.5. Hence, the value of median is verified.

21. Graphs Of Statistics There Are 5 Types Of Graph Commonly Used In Representing Statistical Data The Graphs which are used are :- Bar Graph Double Bar Graph Frequency Distribution Table Frequency Polygon Histogram

22. Bar Graph Uses Of Bar Graph :- M arketing Climate Figures Finance, Etc

23. Double Bar Graph Uses Of Double Bar Graph :- Comparing Result Comparing Score Of 2 Different Teams Comparing Data Of This Year With Previous Year, etc

24. Frequency Distribution Table Uses Of Frequency Distribution Table :- Comparing Marks Of Different Students in a Class Comparing Different Information Such as Height of Students, Weight, etc

25. Frequency Polygon Uses Of Frequency Distribution Table :- Comparing Runs of 2 Different Teams in Cricket Comparing Growth of Companies Comparing Temperature, etc

26. histogram Uses Of Bar Graph :- to tell relative frequency of occurrence to easily see the distribution of the data to make future predictions based on the data, etc