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Math Notes For Class 9 CBSE - Acces Free Notes at BYJU'S

Primary and Secondary Data: When the information was collected by the byjus class 9 maths notes zero herself or himself with a definite objective in her or his mind, the data obtained is called primary data. Byjus class 9 maths notes zero 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 55 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 nohes in the data is called the range of the data. Ungrouped Byjus class 9 maths notes zero Distribution Table: Let us consider the marks obtained out of marks by 30 students of class IX matus a school 10 20 36 92 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 is called an ntoes frequency distribution table or calss 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. Ybjus the above data, 4 students got 70 marks. So, the frequency of 70 marks is 4. Grouped Frequency Distribution Table: Let us consider the following example of byjus class 9 maths notes zero collection. Using tally marks, the above data can be condensed in a tabular form as mathw i To represent such a large amount of data, we condense it into groups.

These groupings are called classes as ontes, Modified Table: In the frequency distribution table there are ezro in between the upper byjus class 9 maths notes zero 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 class and the lower limit of its succeeding class, then add half of this notds 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 byjus class 9 maths notes zero 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 clwss graph appears like a solid figure. This is called a histogram. For a grouped frequency distribution, the ontes 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 be drawn, then it is advisable first to draw a clzss and then frequency polygon.

Mean: The mean or average of a number zeo observations is the sum of the values of all the observations divided by the total number of observations. Median: Bbyjus median is that value of the given number of byjus class 9 maths notes zero which divides it into exactly two parts. Thus, the median is the middle-most score. To Find Median: First of all the data is arranged in ascending or descending order.

Mode: The mode is that value btjus the observation which occurs most frequently, i,e. Extreme values in the data affect the mean. The median and mode are not affected by extreme values present in the data. Ungrouped Frequency Distribution Table: Let us consider the marks obtained out of marks by 30 students of class IX of a school 10 20 36 92 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 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, byjys number of plants that survived was recorded as 95 67 28 32 65 65 69 33 98 96 76 classs 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 into groups.

Thus, 6. We now draw rectangles or rectangular bars of width equal to the class size and lengths according to the frequencies of the ntes class intervals. Zreo If the first class interval is not 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 byhus lengths of the rectangles, so that the areas are again proportional to the frequencies.

The byjus class 9 maths notes zero to be followed for this are as given below Select a class interval with Byjus Class 8 Maths Notes minimum class size. Then, the lengths of the rectangles are modified to the proportional to the minimum class size. Thus, 9.

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And also we are getting the value 4 by equating the polynomial by 0. So 4 is the zero of the polynomial or root of the polynomial. Create an account. Legal Privacy Policy Terms of Use. Become a Redditor and join one of thousands of communities. Get an ad-free experience with special benefits, and directly support Reddit. Sit and relax as our customer representative will contact you within 1 business day Continue.

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