The EB bill(in ₹) of each of the 26 houses in a village are given below. Construct the frequency table. 215 200 120 350 800 600 350 400 180 210 170 305 204 220 425 540 315 640 700 790 340 586 660 785 290 300

From given: Maximum bill amount = ₹ 800 Minimum bill amount = ₹ 120 Range = largest value - smallest value ∴ Range = 800 - 120 = ₹ 680 Suppose if we want to take class size as 100 , then The number of possible class intervals = R a n g e C l a s s s i z e = 680 100 = 6 . 8 ≃ 7 ClassIntervals TallyMarks Frequency 100 - 200 | | | 3 200 - 300 | | | | | 6 300 - 400 | | | | | 6 400 - 500 | | 2 500 - 600 | | 2 600 - 700 | | | 3 700 - 800 | | | | 4 Total 26

Convert the given discontinuous series into a continuous series. Class 0 - 5 6 - 11 12 - 17 18 - 23 24 - 29 Frequency(f) 7 10 9 5 12

Given discontinuous series is: Class 0 - 5 6 - 11 12 - 17 18 - 23 24 - 29 Frequency(f) 7 10 9 5 12 We know that, A continuous data is any value within a certain interval. The data can take values between certain range with the highest and the lowest value. First we should fill the gap by extending the two limits of each class by half of the value of the gap. Here the gap is 1 , so subtracting and adding half of the gap i.e 0 . 5 to the lower and the upper limit of each class makes it as a continuous series. Class - 0 . 5 - 5 . 5 5 . 5 - 11 . 5 11 . 5 - 17 . 5 17 . 5 - 23 . 5 23 . 5 - 29 . 5 Frequency (f) 7 10 9 5 12

Draw a histogram for the following table which represents the age groups from 100 people in a village. Ages 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 Number of people 11 9 8 20 25 10 8 6 3

Given: Ages 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 Number of people 11 9 8 20 25 10 8 6 3 We know that, A histogram is a graph of a continuous frequency distribution. Histogram contains a set of rectangles, the base of which is the length of the class interval and the frequency in each class interval is its height. Follow the below steps to construct Histogram: The given data is a continuous frequency distribution. The class intervals are drawn on x-axis and their respective frequencies on y-axis. Classes (ages) and its frequencies (number of people) are taken together to form a rectangle. Each of the classes have upper and lower values. This gives us equal vertical lines representing the frequencies. The histogram is constructed as given below.

The following table gives the number of literate females in the age group 10 to 45 years in a town. Age group 10 - 15 16 - 21 22 - 27 28 - 33 34 - 39 40 - 45 No. of females 350 920 850 480 230 200 Draw a histogram to represent the above data

Given, Age group 10 - 15 16 - 21 22 - 27 28 - 33 34 - 39 40 - 45 No. of females 350 920 850 480 230 200 We know that, A histogram is a graph of a continuous frequency distribution. Histogram contains a set of rectangles, the base of which is the length of the class interval and the frequency in each class interval is its height. The given distribution is discontinuous. If we represent the given data as it is by a graph we shall get a bar graph, as there will be gaps in between the classes. So, convert this into a continuous distribution using the adjustment factor 0 . 5 . The first class interval can be written as 9 . 5 - 15 . 5 and the remaining class intervals are changed in the same way. There are no changes in frequencies. The new continuous frequency table is Age group 9 . 5 - 15 . 5 15 . 5 - 21 . 5 21 . 5 - 27 . 5 27 . 5 - 33 . 5 33 . 5 - 39 . 5 39 . 5 - 45 . 5 No of females 350 920 830 480 230 200 The histogram is constructed as given below.

Draw a frequency polygon for the following data using histogram. Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of students 5 8 10 18 25 22 20 13 6 3

Given, Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Number of students 5 8 10 18 25 22 20 13 6 3 We know that, A frequency polygon is a line graph for the graphical representation of the frequency distribution. If we mark the midpoints on the top of the rectangles in a histogram and join them by straight lines, the figure, so formes is called frequency polygon. It is called a polygon as it consists of a number of lines as the sides of a polygon. Follow below steps as shown: Mark the class intervals along the x-axis and the number of students along the y-axis . Draw a histogram for the given data and mark the midpoints of the rectangles and join them by lines. We get frequency polygon. Note that the first and last edges of the frequency polygon meet at the mid points of the left and right vertical edges of first and last rectangles. Because imagined class intervals do not exist in the marks (refer the above note).

Draw a frequency polygon for the following data without using histogram. Class interval (Marks) 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 Frequency 4 6 8 12 10 14 5 7

Follow the below steps to draw frequency polygon without using histogram. Find the midpoint of the class intervals and tabulate it. Class interval (C.I) Mid point ( x ) Frequency (f) 10 - 20 15 4 20 - 30 25 6 30 - 40 35 8 40 - 50 45 12 50 - 60 55 10 60 - 70 65 14 70 - 80 75 5 80 - 90 85 7 The points are A ( 5 , 0 ) B ( 15 , 4 ) C ( 25 , 6 ) D ( 35 , 8 ) E ( 45 , 12 ) F ( 55 , 10 ) G ( 65 , 14 ) H ( 75 , 5 ) I ( 85 , 7 ) J ( 95 , 0 ) . In the graph sheet, mark the midpoints along the x - axis and the frequency along the y - axis. We take the imagined class as 0 - 10 at the beginning and 90 - 100 at the end, each with frequency 'zero'. From the table, plot the points. We draw the line segments AB , BC , CD , DE , EF , FG , GH , HI , IJ to obtain the required frequency polygon ABCDEFGHIJ .

E M B I B E

Standard Eight Mathematics>Chapter 6 - Statistics>Exercise 6.3>Q 7

MEDIUM

8th Tamil Nadu Board

IMPORTANT

Earn 100

Draw a histogram for the following data.

Mid Value $(x)$ $15$ $25$ $35$ $45$ $55$ $65$ $75$

Frequency $(f)$ $12$ $24$ $30$ $18$ $26$ $10$ $8$

Important Questions on Statistics

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8th Tamil Nadu Board

IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 2

The EB bill(in ₹) of each of the 26 houses in a village are given below. Construct the frequency table.

$\begin{array}{l} 215 & 200 & 120 & 350 & 800 & 600 & 350 & 400 & 180 & 210 & 170 & 305 & 204 \\ 220 & 425 & 540 & 315 & 640 & 700 & 790 & 340 & 586 & 660 & 785 & 290 & 300 \end{array}$

EASY

8th Tamil Nadu Board

IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 3

Convert the given discontinuous series into a continuous series.

$\begin{array}{lccccc} Class & 0 - 5 & 6 - 11 & 12 - 17 & 18 - 23 & 24 - 29 \\ Frequency(f) & 7 & 10 & 9 & 5 & 12 \end{array}$

MEDIUM

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IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 5

Draw a suitable pie chart for the following data relating to the cost of construction of a house.

$\begin{matrix} Particulars & Bricks & Steel & Cement & Timber & Labour & Others \\ Expenses: & 10 % & 15 % & 25 % & 10 % & 20 % & 20 % \end{matrix}$

Also, find how much was spent on labour if $₹ 55000$ was spent for cement.

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8th Tamil Nadu Board

IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 6

Draw a histogram for the following table which represents the age groups from $100$ people in a village.

$\begin{array}{lccccccccc} Ages & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 \\ Number of people & 11 & 9 & 8 & 20 & 25 & 10 & 8 & 6 & 3 \end{array}$

MEDIUM

8th Tamil Nadu Board

IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 7

The following table gives the number of literate females in the age group $10$ to $45$ years in a town.

$\begin{array}{lcccccc} Age group & 10 - 15 & 16 - 21 & 22 - 27 & 28 - 33 & 34 - 39 & 40 - 45 \\ No. of females & 350 & 920 & 850 & 480 & 230 & 200 \end{array}$

Draw a histogram to represent the above data

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IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 9

The following is the distribution of time spent in the library by students in a school.

$\begin{array}{lcccccccc} Time spent (in minutes) & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 \\ Number of Students & 25 & 40 & 33 & 28 & 30 & 20 & 16 & 8 \end{array}$

Draw a frequency polygon using histogram.

MEDIUM

8th Tamil Nadu Board

IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 10

Draw a frequency polygon for the following data using histogram.

$\begin{array}{lcccccccccc} Marks & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 \\ \begin{array}{l} Number of \\ students \end{array} & 5 & 8 & 10 & 18 & 25 & 22 & 20 & 13 & 6 & 3 \end{array}$

EASY

8th Tamil Nadu Board

IMPORTANT

Standard Eight Mathematics>Chapter 6 - Statistics>Example>Q 11

Draw a frequency polygon for the following data without using histogram.

$\begin{matrix} Class interval (Marks) & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 \\ Frequency & 4 & 6 & 8 & 12 & 10 & 14 & 5 & 7 \end{matrix}$