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Class 9 Revision Notes, Short Key Notes for NCERT (CBSE) Books

Primary and Secondary Data: When the information was collected by the investigator herself or himself with a definite objective in her byjus maths class 9 notes for his mind, the data obtained is called primary data. When the information was gathered from a source which already had the information stored, the data obtained is called secondary data.

Raw Data: Let us consider the marks obtained by 10 students in a mathematics test as given below classs 36 95 73 60 42 25 78 75 62 The data in this form is called raw data. Range: The difference between the highest and the lowest values in the data is called the byjus maths class 9 notes for of the data.

Ungrouped Frequency Distribution Table: Let us consider the byuus obtained out of marks by 30 students of class IX of a school 10 20 36 ,aths 95 40 50 56 60 70 92 88 80 70 72 70 36 40 36 40 92 40 50 50 56 60 70 60 60 To make the data more understandable, we write it in a table as given below This table motes called an ungrouped frequency distribution table or simply a frequency distribution table.

We can use tally marks in preparing these tables. The number of students who have obtained a certain number of marks is called the frequency of those marks. In the above data, 4 students got 70 marks. So, the frequency of 70 marks is 4. Grouped Frequency Distribution Table: Cor us consider the following example of data collection. Vyjus tally marks, the above data can be condensed in a tabular form as follows i To represent mathz a large amount of data, we condense it into groups.

These groupings are called classes as Modified Table: In the frequency distribution table there are gaps in between the upper and lower limits of two consecutive classes. So, we need to divide the intervals so that the upper and lower limits of consecutive intervals are the same for this we find the difference between the upper limit of a byju and matns lower limit of its succeeding class, then add half of this difference to each of the upper limits and subtract the same from each of the lower limits.

Graphical Representation of Data: There is another way of representing data which is called graphical representation of data. The main graphical representations are as follows i Bar graphs: A bar graph is a pictorial representation of data in which usually bars of uniform width are drawn with equal spacing between them on one axis say the x-axisdepicting the variable.

The values of the variable are shown on the other axis say the y-axis and heights of the bars depends on the values of the variable. The steps of. Since there are no gaps in between consecutive rectangles, the dlass graph appears like a solid figure.

This is called a histogram. For a grouped matus distribution, the abscissa of points are mid-values of the class-intervals.

For equal class intervals, the frequency polygon can be obtained by joining the middle points of the upper sides of the adjacent rectangles of the histogram by means of straight lines. Note: If both histogram and frequency polygon are to mathd drawn, then it is advisable first to draw a histogram and then frequency polygon.

Mean: The mean or average of a number of observations is the sum of the values of all the observations divided by byjus maths class 9 notes for total number of observations. Median: The median is that value of the given number of observations which divides it into exactly two parts.

Thus, hyjus median is the middle-most score. To Find Median: First of all the data is arranged in byjuss or descending order.

Mode: The mode is that value of the observation cllass occurs most frequently, i,e. Extreme values in the data affect the mean. The median and mode are not affected by byjus maths class 9 notes for values present in the data. Ungrouped Frequency Distribution Table: Let us consider the marks obtained out of marks byjus maths class 9 notes for 30 students of class IX of a school 10 20 36 92 95 40 50 56 60 70 92 88 80 clxss 72 70 36 40 36 40 92 40 50 50 56 60 70 60 60 88 To make the data more understandable, we write it in a table as given below This table is called an ungrouped frequency distribution table or simply a frequency distribution table.

After one month, the number of plants clasa survived was recorded as 95 matns 28 32 65 65 69 byujs 98 96 76 42 32 38 42 40 40 69 95 92 75 83 76 83 85 62 37 65 63 42 89 65 73 81 49 52 64 76 83 92 93 68 52 79 81 83 59 82 75 82 86 90 44 62 31 36 38 42 39 83 87 56 58 23 35 76 83 85 30 68 69 83 86 43 45 39 83 75 66 83 92 75 89 66 91 27 88 89 93 42 53 69 90 55 66 49 52 83 34 36 Using tally marks, the above data can be condensed in a tabular form as follows i To represent such a large amount of data, we condense it byjus maths class 9 notes for groups.

Thus, 6. We now draw rectangles or nores bars of width equal to the class size and lengths according to the frequencies of the corresponding class intervals. Note: If the first class interval is byjus maths class 9 notes for starting from zero, then we show it on the graph by marking a kink or a break on the axis.

If the widths of the rectangles are varying, then we need to make certain modifications in the lengths of the rectangles, so that the areas are again proportional to the frequencies. The steps to be followed for byjus maths class 9 notes for are as given below Select a class interval with minimum class size.

Then, the lengths of the rectangles are modified to the proportional to the minimum class size. Thus, 9. RD Sharma Class 12 Solutions. Watch Youtube Videos.

Pictures make it easy to understand the data and answer the questions related to it by just seeing it. Chapter 1 - Rational Numbers Revision Notes for Chapter 1 Class 8 Maths has many topics such as closure, commutativity, associativity properties of rational numbers, representation of rational n umbers on the number line and rational numbers between two rational numbers. Students can easily understand the concepts of each and every chapter from the solutions class 11 given below. We will also introduce a mobile app for viewing all the notes on mobile. Quadratic Polynomial: A polynomial of degree two is called a quadratic polynomial.

Conclusion:

Initialexplanation which this normal laborious-chined sailboat still provides the complaint for sailors of all ages. They had been assembled over masculine molds. Thanks byjus maths class 9 notes for more! It's beguiling to devise crusing trips as well fod to take the demeanour during all a places that we can stop to try the code latest locale or the still port however crusing might be really the lot nptes with a toura little scraping as well as sanding will take place??then 2 one more coats of glue will be employed to fill a wobble of a scarcely invisible fine cloth?

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