Statistics is an important chapter for class 9 NCERT Maths. You must have studied concepts like mean, average, frequency and graphs in previous classes as well, Statistics class 9 is an extension of these concepts. The chapter explains its true meaning and draws light on some real life implementation of Statistics. This blog has all the essential details and study notes to get full marks in Statistics class 9.
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What is statistics?
Statistics is a branch of mathematics that deals with collecting, organising, and interpreting data. It has become useful in all branches of knowledge. Predictions and estimates are usually made with the help of Statistics. To understand the meaning of Statistics, you need to understand all its factors. Data is one of the most important elements of Statistics class 9. Let us understand its meaning in the next section.
A piece of information in the form of facts or figures collected for a specific purpose is known as data. It is of 2 types:
1.Primary data – When the statistical investigator collects the information for the first time with a definite purpose in mind, it is known as primary data.
2.Secondary data – When the data is obtained from a third party or a source that already contains the data, it is known as secondary data.
3. Raw Data – Let us consider the marks obtained by 12 students in a physics test as given below
25, 67,35,78,32, 78,72, 69, 98,51,89, 40
Data in the above-mentioned form is known as Raw Data.
4. Range – The difference between the lowest and the highest values in data is known as the range of the data.
Range= Highest value – Lowest Value
5. Ungrouped Frequency Distribution Table – Let us observe the marks scored by 30 class 8 students in a surprise English test
36, 80,92,95, 10,20, 40, 50, 56, 60, 70,80
88, 92, 70,80, 70,72, 40,36, 40,36,80
92,80, 80, 40, 50,50, 56, 60, 70, 60,60, 88
To make this data more understandable we write it in a table, as given below:
|Marks ||Number of Students(the frequency)|
- Such a table is called an Ungrouped Frequency Distribution Table. We can even use tally marks for preparing such tables.
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Presentation of data
Once the data has been collected, it is essential to present it in a meaningful manner. There are various ways of data presentation.
This type of data is presented in the original form in which it is collected. The data is not sorted by any method. For example, the marks obtained by 10 students in an exam are 22, 50, 32, 43, 15, 45, 49, 25, 38, 19. This is also known as raw data.
When the data is divided into groups or classes, it is known as grouped data.
The group, or the class size, which is used to divide the data, is known as the class interval. It can be of 2 types:
Regular – When every class interval is of the same size, such as 1-5, 6-10, 11-15, 16-20
Irregular – When the class intervals are of different sizes, such as 1-5, 5-20, 20-50, 50-100.
The number of times a particular data occurs is known as frequency.
Frequency distribution table
It is a table that represents the frequency or the occurrence of variables in a piece of data. It is of 2 types:
– Grouped frequency table – The frequencies are arranged in a particular manner, either ascending or descending.
– Ungrouped frequency table – When the frequencies are not arranged in any manner, it is known as ungrouped frequency.
Graphical Representation of Data
This is the easiest way of data representation for statistics class 9. The total numerical value of data can be visualised in the form of graphs. Various types of graphs can be used to represent data. Some of them are given below.
- Bar graph – These graphs use rectangular bars to represent data. It is the simplest and most widely used method. The width and space between the bars should be the same. The height of the bars is adjusted according to the numerical value that they represent.
- Histogram – It is similar to a bar graph but is used only for continuous class intervals. There are no gaps between the rectangular bars. Hence, it looks like a solid figure. Each bar area is directly proportional to the frequency of the variable, whereas the width is equal to the class interval.
- Frequency polygon – If the midpoints of the bars in a histogram are joined together by a line, it represents a frequency polygon. A frequency polygon can be drawn with or without a histogram. The midpoint of the first and the last bar is joined to the x-axis.
Also Read: Application of Statistics
Measures of Central Tendencies
To make the collection of data useful, there are three measures of central tendency –
- Mean – It is calculated by dividing the sum of the observations by the total number of observations. It is represented by the symbol x bar.
- Median – It is the mid-value of the observations that divide the observations into two equal parts. The formula is different for odd and even numbers of observations. Another method of finding the median is by arranging the values in ascending order, and then the value that comes in the middle is the median.
- Mode – The mode is that value among the observations, which occurs most frequently in the data. The number that has the maximum value is the mode. For example, in the given observations 21, 34, 55, 65, 78, 76, 21, 34, 21, 21, 54, 64, 87, 21. 21 is the mode as it appears most frequently.
1. Give three examples of data which you get in your day to day life.
The three examples of date which we get in our day to day life are:
Electricity bills of the past one year
Number of girls in our hockey team
Number of students appearing for board exam from our school
Find the mean number of family members per room.
Number of family members per 10 rooms – 2,4,3,3,1,0,2,4,1,5
Therefore, we get,
Mean = (2+4+3+3+1+0+2+4+1+5)/10
Mean = 25/10 = 2.5
105,216, 322, 167, 273, 405 and 346
Find the average number of coupons issued per day.
Number of coupons issed in a week: 105,216,322,167,273,405, 346
Mean= sum of observation/total number of observations
Mean= 105+216+322+167+273+405+346/7 = 1834/7
Find the median weight.
First, let us arrange the data in ascending order – 44, 45,49,50,52,55,60
Median= (n+1)/ 2 observations
= (7+1) / 2 = (8/2) observation = 4th observation = 50 kg
Mean = sum of observations / total number of observations
13= (y + y+1+y+4+y+6+y+8+y+5)/ 6
13= (6y+24)/ 6
13*6 = 6y + 24
13*6 – 24 = 6y
13*6 – 6*4 = 6y
6(13-4) = 6y
Y = 9
Mean of 36 notice = 12
Total of 36 notices = 36x 12 = 432
Correct sum of 36 noticess = 432 – 74 + 47 = 405
Correct mean of 36 notices = 405/36 = 11.25
Since the mean of 20 observations is 17
Sum of 20 observations = 17 x 20 = 340
New sum of 20 observations = 340-40 +12 = 312
New Mean = 312/20 = 15.6
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Statistics is an essential branch of mathematics used in almost every field. Hence, statistics class 9 is an important chapter for the students. Hope these study notes made the entire process of understanding the topic better for you. Reach out to Leverage Edu experts in case of any career or course related query.