Statistics Class 9

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Statistics Class 9

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

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.

What is Data?

A piece of information in the form of facts or figures collected for a specific purpose is known as data. It is of the following 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

Frequency Distribution Table

In Statistics class 9, a frequency distribution is a list, table (i.e.: frequency table) or graph (i.e.: bar plot or histogram) that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval. They are of two types:

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)
10 1
20 1
36 2
40 4
50 3
56 2
60 4
70 3
80 7
88 2
92 1
Total  30
  • Such a table is called an Ungrouped Frequency Distribution Table. We can even use tally marks for preparing such tables. 

Grouped Frequency Distribution Table

Let us consider the following example of data collection. 100 plants each were planted in 100 schools during Van Mahotsava Annual Event Tree plantation drive. After one month, the number of plants that survived was recorded as:

95 67 28 32 65 65 69 33 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

The above data can be condensed in a tabular form as follows:

Number of Plants Survived  Number of Schools (frequency)
20-29 3
30-39 14
40-49 12
50-59 8
60-69 18
70-79 10
80-89 23
90-99 12
Total  100

Note: We reduce such a vast amount of data into groups to represent it. These groups are referred to as classes such as 20-29, 30-39 and so on. The lowest number in a class is known as the lower class limit, while the highest number is known as the upper-class limit, as in 20-29, where 20 is a lower class limit and 29 is an upper-class limit. The class interval is the difference between the lower and upper-class limits. The midpoint of a class is referred to as the class mark. Thus,

Statistics Class 9 Notes Maths Chapter 14 3
Courtesy: NCERT, Statistics Class 9

Also Read: Surface Area And Volume Class 10 Maths

Modified Table

There are gaps in the frequency distribution table between the top and lower limits of two successive classes. So, we need to divide the intervals so that the upper and lower limits of consecutive intervals are the same. To do this, we find the difference between a class’s upper limit and the 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.

For example, consider two consecutive classes 11-15 and 16-20.

Then, difference = 16 – 15 = 1

Half of the difference = ½ = 0.5

So, the new class interval formed are:

  • 11-15 is now 10.5-15.5 
  • 16-20 is now 15.5-20.5

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.

  1. 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.
Credits: Basic Mathematics
  1. 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.
Courtesy: Online Math Learning
  1. 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.
Courtesy Math Only Math

Also Read: Application of Statistics

Measures of Central Tendencies

To make the collection of data usage, there are three measures of central tendency –

  1. 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.
  1. 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.
  1. 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.

Statistics Class 9 NCERT PDF

Statistics Class 9 PPT

Courtesy: Navin Patle

Also Read: Class 9 Polynomials

Statistics Class 9 Important MCQs

  1. The number of times particular items occur in a class interval is called its:

A. Mean

B. Frequency

C. Cumulative frequency

D. Range

  1. The range of the data 25.7, 16.3, 2.8, 21.7, 24.3, 22.7, 24.9 is:

A. 22

B. 22.9

C. 21.7

D. 20.5

  1. If the class marks in a frequency distribution are 19.2, 26.5, 33.5, 40.5, then the class corresponding to the classmark 33.5 is:

A. 16-23

B. 23-30

C. 30-37

D. 37-41

  1. There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be –3.5. The mean of the given numbers is:

A. 46.5

B. 49.5

C. 53.5

D. 56.5

  1. If the mean of the observations: x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observations is:

A. 10 ⅓ 

B. 10 ⅔ 

C. 11 ⅓ 

D. 11 ⅔ 

  1. The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is:

A. 6

B. 5

C. 3

D. 2

  1. A grouped frequency distribution table with classes of equal sizes using;63-72 (72 included) as one of the class is constructed for the following data:

30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88,

40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96,

102, 110, 88, 74, 112, 14, 34, 44

The number of classes in the distribution will be:

A. 9

B. 10

C. 11

D. 12

  1. Let m be the mid-point and l be the upper-class limit of a class in a continuous frequency distribution. The lower class limit of the class is:

A. 2m + l

B. 2m – l

C. m – l

D. m – 2l

  1. The width of each of the five continuous classes in a frequency distribution is 5 and the lower class limit of the lowest class is 10. The upper class-limit of the highest class is:

A. 15

B. 25

C. 35

D. 40

  1.  Parvati obtained 16, 14, 18 and 20 marks (out of 25) in English in weekly tests in the month of Jan. 2000. The mean marks of Parvati is:

A. 15

B. 17.5

C. 17

D. 18.5

Answers 

  1. C
  2. D
  3. C
  4. D
  5. C
  6. B
  7. C

Statistics Class 9 Important Questions & Answers

1. Give three examples of data that you get in your day to day life.

The three examples of data that we get in our day to day life are:
Electricity bills of the past year
Number of girls in our hockey team
Number of students appearing for board exam from our school

2. The number of family members in Gaurav’s family in 10 rooms are
2,4,3,3,1,0, 2,4,1,5
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

3. The following is the list of a number of coupons issued in the school fete during a week:
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
= 262

4.The weight of 7 adults in a sports competition is 49,45,52, 44, 55,60,50.
Find the median weight.

First, let us arrange the data in ascending order – 44, 45,49,50,52,55,60
n= 7
Median= (n+1)/ 2 observations
= (7+1) / 2 = (8/2) observation = 4th observation = 50 kg

5. If the mean of six observations y,y+1, y+4, y+6, y+8, y+5 is 13, find the value of y.

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

6. Mean of 36 notices is 12. One notice 47 was misread as 74. Find the correct mean.

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

7. Mean of 20 observations is 17, if in the observation 40 is replaced by 12, find the new mean.

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

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.

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