SEBA Class 9 Mathematics Chapter 14 Statistics

SEBA Class 9 Mathematics Chapter 14 Statistics Solutions, SEBA Class 9 Maths Textbook Notes in English Medium, SEBA Class 9 Mathematics Chapter 14 Statistics Solutions in English to each chapter is provided in the list so that you can easily browse throughout different chapter Assam Board SEBA Class 9 Mathematics Chapter 14 Statistics Notes and select needs one.

SEBA Class 9 Mathematics Chapter 14 Statistics

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Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. SEBA Class 9 Mathematics Chapter 14 Statistics Question Answer. These solutions are part of SCERT All Subject Solutions. Here we have given SEBA Class 9 Mathematics Chapter 14 Statistics Solutions for All Subject, You can practice these here.

Statistics

Chapter – 14

1. Give five examples of data that you can collect from your day-to-day life.

Ans: (i) Number of students in our class.

(ii) Number of fans in our school.

(iii) Electricity bills of our house for the last two years.

(iv) Election results obtained from television newspapers.

(v) Literacy rate figures obtained from educational surveys.

2. Classify the above data as primary or secondary data.

Ans: (i), (ii) and (iii) are primary data. (iv) and (v) are secondary data.

1. Presentation of Data

As soon as the work related to collection of data is over, the investigator has to find out ways to present them in a form which is meaningful, easily understood and gives its main features at a glance.

2. Various Ways of Presenting the Data

(i) Raw data. Let us consider the marks obtained by 10 students in a mathematics test as given below:

The data in this form is called raw data.

Demerit of Raw Data. From raw data, we take some time in searching for the maximum and minimum scores.

The above marks arranged in ascending order are as follows:

It is easily clear that 

Lowest marks = 25 

Highest marks = 95

Range. The difference of the highest and the lowest values in the data is called the range of the data.

So, the range in this case is 95-25 = 70

Demerit of Data in Ascending (Descending Order)

Presentation of data in ascending or descending order can be quite time consuming, particularly when the number of observations in an experi- ment is large.

(ii) Ungrouped frequency distribution table. Let us consider the marks obtained (out of 100 marks) by 30 students of Class IX of a school.

Frequency. The number of students who have obtained a certain number of marks is called the frequency of those marks. For example, 4 students got 70 marks. So the frequency of 70 marks is 4. 

Tabular Form. To make the data more understandable, we write it in a table as given below:

This table is called an ungrouped an ungrouped frequency distribu- tion table or simply a frequency distribution table. We can use tally marks in preparing these tables.

Demerit. With a large amount of data, the formation of such a table becomes difficult and time consuming.

(iii) Grouped frequency distribution table. Let us consider the following example of data collection.

100 plants each were planted in 100 schools during Van Mahotsava After one month, the number of plants that survived were recorded as:

Classes. To present such a large amount of data, so that a reader can make sense of it easily, we condense it into groups. Their groupings are called ‘classes’ or ‘class-intervals’, and their size is called the class-size or class width, or class-interval. We here take groups like 20-29, 30-39,… 90-99 (since our data is in between 22 and 99) of size 10.

Lower/Upper class limits. The least number of a class is called the lower class limit and the greatest number is called the upper class limit. For example: In 20-29, 20 is the ‘lower class limit’ and 29 is the ‘upper class limit’.

Class Mark. The midpoint of a class is called the class mark of Thus, class.

larly class-marks of subsequent classes are 34.5, 44.5,…, 94.5.

TABLE

Merit. Presenting data in this form simplifies and condenses data and enables us to observe certain importance features at a glance. This is called a Grouped frequency distribution table. Here we can easily observe that 50% or more plants survived in 8 + 18 + 10 + 23 + 12 = 71 schools.

Non-overlapping classes. We observe that the classes in the table above are non-overlapping. Note that we could have made more classes, of shorter size, or fewer classes of larger size also. For instance, the intervals could have been 22-26, 27-31, and so on, So, threre is no hard and fast rule about this except that the classes should not overlap.

Demerit. In certain cases, we might have required to include data lying between the upper limit of a class and lower limit of the consecutive class. This is not possible in this table. So we need to modify this table as explained below:

Modified Table. Let us now consider the following frequency distribution table which gives the weights of 38 students of a class:

Table

Now, if two new students of weights 35.5 kg and 40.5 kg are admitted in this class, then we cannot add them in these intervals ending with 35 or 40, nor to the following ones. This is because 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 class and the lower limit of its succeeding class. We then add half of this differ-ence to each of the upper limits and subtract the same from each of the lower limits.

Fr example, consider the classes 31-35 and 36-40

The lower limit of 36-40 = 36

The upper limit of 31-35 = 35

The difference = 36-35 = 1

So the new class interval formed from 31-35 is (31-0.5 is (31-0.5) – (35+0.5) 30.5-35.5

Similarly, the new class formed from the class 36-40 is (36-0.5)-(40+0.5) = 35.5-40.5

Continuing in the same manner, the continuous classes formed are: 30.5-35.5, 35.5-40.5, 40.5-45.5, 45.5-50.5, 50.5-55.5, 55.5- 60.5, 60.5-65.5, 65.5-70.5, 70.5-75.5 These are called true class limits.

Now it is possible for us to include the weights of the new students in these classes. But, another problem crops up as 35.5 appears in both the classes 30.5-35.5 and 35.5-40.5.

If it is considered in both classes, it will be counted twice.

By convention, we consider 35.5 in the class 35.5-40.5 and not in 30.5-35.5. Similarly, 40.5 is considered in 40.5-45.5 and not in 35.5-40.5.

So, the new weights 35.5 kg and 40.5 kg would be included in 35.5- 40.5 and 40.5-45.5, respectively. Now, with these assumptions, the new (modified) frequency distribution table will be as shown below:

TABLE

3. Cumulative Frequency and Cumulative Frequency Table

The total of frequencies of a particular class and of all classes prior to that particular class is called the cumulative frequency of that class. 

For calculating cumulative frequencies, the classes should be written in ascending order.

A table which displays the manner in which cumulative frequencies are distributed over various classes is called a cumulative frequency (dis-ribution) table.

Example. Consider a frequency distribution table as follows:

Then the cumulative frequency table for the above data is as follows:

Note. The cumulative frequency of the last class is the total number of Frequencies or the total number of observations in the data in the raw form.

Q. Mid Value of the class interval 85-90 is 

(a) 89.9

(b) 85.5

(c) 87.5

(d) 86.5

Ans: (c) 87.5

1. The blood groups of 30 students of class VIII are recorded as follows:

A, B, O, O, AB, O, A, B, A, O, B, A, O, Ο

A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.

Represent this data in the form of a frequency distribution table. Find out which is the most common and which is the rarest blood group among these students.

Ans: 

O is the most common and AB is the rarest blood group among these students.

2. The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

Construct a grouped frequency distribution table with class size 5 for the data given above, taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular rep-resentation?

Ans: 

We observe the following main features from this tabular repre-sentation:

(i) The distance (in km) from their residence to their workplace of the maximum number of female engineers are in the third interval, i.e., 10-15.

(ii) The distances (in km) from their residence to their workplace of the minimum number of female engineers are in the intervals 20-25 and 25-30 cách.

(ii) The frequencies of the intervals 20-25 and 25-30 are the same. (Each = 1)

3. The relative humidity (in %) of a certain a certain city for a month of 30 days was as follows:

(i) Construct a grouped frequency distribution table with classes 84-86, 86-88, etc.

Ans: 

(ii) Which month or season do you think this data is about?

Ans: This data is about the month of June (Rainy season)

(iii) What is the range of this data?

Ans: Range Highest value – Lowest value = 99.2-84.9 = 14.3 (in %)

4. The heights of 50 students, measured to the nearest centimetre, have been found to be as follows:

(i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160-165, 165-170, etc.

Ans: 

(ii) What can you conclude about their heights from the table?

Ans: The heights of maximum number of students are in the group 160-165 and the heights of minimum number of students are in the group 170-175.

5. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows:

(i) Make a grouped frequency distribution table for this data with class intervals as 0.00-0, 0.04, 0.04-0.08 and so on.

Ans: 

(ii) For how many days, was the concentration of sulphur dioside more than 0.11 parts per million?

Ans: The concentration of sulphur dioxide was more than 0.11 parts per million for 2+4+28 days.

6 Three coins were tossed 30 times simultaneously. Each time the number of heads occuring was noted down as follows:

Prepare a frequency distribution table for the data given above.

Ans: 

7. The value of π upto 50 decimal places is given below: 

3.14159265358979323846264338327950288419716939937510

(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.

Ans: 

(ii) What are the most and the least frequently occurring digits?

Ans: The most frequently occuring digits are 3 and 9. The most least frequently occurring digit is 0.

8. Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5-10.

Ans:  

(ii) How many children watched television for 15 or more hours a week?

Ans: 2 children watched television for 15 or more hours a week.

9. A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2-2.5.

Ans: 

1. A survey conducted by an organisation for the cause of illness and death among the women between the ages 15-44 (in years) worldwise, found the following figures (in %):

(i) Represent the information given above graphically.

Ans: 

(ii) Which condition is the major cause of women’s ill health and death worldwide?

Ans: Reproductive health conditions are the major cause of women’s ill health and death worldwide.

(iii) Try to find out, with the help of your teacher, any two fac- tors which play a major role in the cause in (ii) above being the major cause.

Ans: Lack of proper diet, lack of advice exercises.

2. The following data on the number of girls (to the nearest ten) per thousand boys in different sections of the society is given below:

(i) Represent the information above by a bar graph.

Ans: 

(ii) In the classroom what conclusion can be arrived at from the graph.

Ans: The two conclusions we can arrive at from the graph are as follows:

(a) The number of girls to the nearest ten per thou- sand boys is maximum in the Scheduled Tribe section of the society and minimum in the Urban section of the society.

(b) The number of girls to the nearest ten per thousand boys is the same for ‘Non SC/ST’ and ‘Non-back- ward Districts’ sections of the society.

3. Given below are the seats won by different political par- ties in the polling outcome of a state assembly elections:

(i) Draw a bar graph to represent the polling results.

Ans: 

(ii) Which political party won the maximum number of seats?

Ans: Political party A won the maximum number of seats. 

4. The length of 40 leaves of a plant are measured correct to one millimetre,and the obtained data is represented in the following table:

(i) Draw a histogram to represent the given data.

(ii) Is there any other suitable graphical representation for the same data?

Ans: (i) Modified continuous Distribution

(ii) Frequency Polygon.

(iii) No because the maximum number of leaves have their lengths lying in the interval 145-153.

5. The following table gives the life times of 400 neon lamps:

(i) Represent the given information with the help of a histo-gram.

Ans: 

(ii) How many lamps have a lifetime of more than 700 hours?

Ans: 74 + 6 2+ 48 = 184 lamps have a lifetime of more than 700 hours.

6. The following table gives the distribution of students of two sections according to the marks obtained by them:

Represent the marks of the students of both the sections on the same graph by frequency polygons.

Ans: Modified

For section A

For section A

7. The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

Represent the data of both the teams on the same graph by fre-quency polygons.

Ans: Modified Table

8. Random survey of the number of children of vari- ous age groups playing in a park was found as follows:

Draw a histogram to represent the data above.

Ans: Modified Table

[Minimum class-size = 1]

9. 100 surnames randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabets in the surnames was found as follows:

(i) Draw a histogram to depict the given information.

Ans: Modified Table

[Minimum class-size = 2]

(ii) Write the class interval in which the maximum number of surnames lie.

Ans: The class interval in which the maximum number of sur- names lie is 6-8.

1. The following number of goals were scored by a team in a series of 10 matches: 

2, 3, 4, 5, 0, 1, 3,4,3 

Find the mean, median and mode of these scores.

Ans: (i) Mean

(ii) Median

Arranging the given data in ascending order, we have

 0, 1, 2, 3, 3, 3, 3, 4, 4, 5

Number of observations (n) = 10, which is even. 

(iii) Mode

Arranging the given data in ascending order, we have 

0, 1, 2, 3, 3, 3, 3, 4, 4, 5 

Here, 3 occurs most frequently (4 times) 

 ∴ Mode = 3

2. In a Mathematics test given to 15 students, the following marks (out of 100) are recorded: 

41, 39, 48, 52, 54, 40, 96, 52, 98, 40 42, 52, 60

Find the mean median and mode of the above marks.

Ans: (i) Mean

(ii) Median

Arranging the given data in descending order, we have 

98, 96, 62, 60, 54, 52, 52, 52, 48, 46, 42, 41, 40, 40, 39 

Number of observations (n) = 15 which is odd. 

(iii) Mode

Arranging the data in descending order, we have

98, 96, 62, 60, 54, 52, 52, 52, 48, 46, 42, 41, 40, 40, 39

Here, 52 occurs most frequently (3 times) 

∴ Mode = 52

3. The following observations have been arranged in as-cending order. If the median of the data is 63, find the value of x.

29, 32, 48, 50, x, x + 2, 72, 78, 84, 95

Ans: Number of observations (n) = 10 which is even. 

According to the question, x + 1 = 63

⇒ x = 63-1 ⇒ x = 62 

Hence the value of x is 62. 

4. Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18

Ans: The given data is 14, 25, 14, 28, 18, 14, 23, 22, 14, 18 

Arranging the data in ascending order, we have 

14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28 

Here 14 occurs most frequently (4 times)

∴ Mode = 14

5. Find the mean salary of 60 workers of a factory from the following table:

Ans: 

Hence the mean salary is Rs. 5083.33 

Q. 6 Give one example of a situation in which:

(i) the mean is an appropriate measure of central tendency.

Ans: means marks in a test in mathematics.

(ii) the mean is not an appropriate measure of central ten-dency but the median is an appropriate measure of central tendency.

Ans: average beauty.