Find the mode of following data, using a histogram. Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 12 20 9 4

Given frequency distribution is:- Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 12 20 9 4 To create a histogram, first we represent the class intervals along the X - axis on a suitable scale and the corresponding frequencies along the Y - axis on a suitable scale. We construct rectangles with class intervals as bases and the corresponding frequencies as heights. Thus, we obtain a histogram as shown below: The process of finding the mode involves few steps: Inside the highest rectangle corresponding to 20 (which represents the modal class 20 - 30 ,we draw two straight lines from the corners of the rectangles on both sides of the highest rectangle to the opposite corners of the highest rectangle. Through, the point of intersection P of the two straight lines drawn in previous step, we draw a vertical line to meet the X - axis at the point M . The x -coordinate at point M is the required mode. Thus, From the histogram, we see that the mode is 24 .

The following table shows the expenditure of 60 boys on books. Expenditure (in ₹) 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 Number of Students 4 7 23 18 6 2 Find the mode of their expenditure.

Given: The frequency distribution is:- Expenditure (in ₹) 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 Number of Students 4 7 23 18 6 2 We have to construct a histogram: To draw a histogram, we represent the class intervals along the x - axis on a suitable scale and the corresponding frequencies along the y - axis on a suitable scale. We construct rectangles with class intervals as bases and the corresponding frequencies as heights. Thus, we obtain a histogram as shown below: Now, to calculate the mode: Inside, the highest rectangle corresponding to 23 (which represents the modal class ( 30 - 35 ) ), we draw two straight lines from the corners of the rectangles on both sides of the highest rectangle to the opposite corners of the highest rectangle. Through, the point of intersection P of the two straight lines drawn , we draw a vertical line to meet the x - axis at the point M (say). The mode is the variate of point ( M ) , that is 34 .

Using a graph paper draw a histogram for the given distribution showing the number of runs scored by 50 batsman. Estimate the mode of the data. Runs scored Number of batsman 3000 - 4000 4 4000 - 5000 18 5000 - 6000 9 6000 - 7000 6 7000 - 8000 7 8000 - 9000 2 9000 - 10000 4

Given: The distribution is shown for the number of runs scored by 50 batsman. We have to find the mode of the data. We need a histogram for this. We represent the class intervals along the X - axis on a suitable scale and the corresponding frequencies along the Y - axis on a suitable scale. We construct rectangles with class intervals as bases and the corresponding frequencies as heights. Thus, we obtain a histogram as shown below Next, we have to determine the mode of this frequency distribution: Inside, the highest rectangle (which represents the class with maximum frequency, i.e. modal class), we draw two straight lines from the corners of the rectangles on both sides of the highest rectangle to the opposite corners of the highest rectangle. Through, the point of intersection of the two straight lines drawn, we draw a vertical line to meet the X - axis at the point M (say). The variate at.the point M is the required mode. Hence, the mode is 4600 .

The marks of 200 students in a test are given below Marks% 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 Number of students 7 11 20 46 57 37 15 7 Draw the histogram and find the mode.

Given; The frequency distribution is given as follows: Marks% 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 No.of students 7 11 20 46 57 37 15 7 Here we see that the frequency distribution is not continuous. In order to make it continuous, we subtract h 2 from the lower limit of each class and add h 2 to the upper limit of each class, where h = 20 - 19 = 1 The continuous frequency distribution for the given data is as follows Marks % 9 . 5 - 19 . 5 19 . 5 - 29 . 5 29 . 5 - 39 . 5 39 . 5 - 49 . 5 49 . 5 - 59 . 5 59 . 5 - 69 . 5 69 . 5 - 79 . 5 79 . 5 - 89 . 5 No.of students 7 11 20 46 57 37 15 7 We will draw the histogram as follows: We represent the class intervals along the X - axis on a suitable scale and the corresponding frequencies along the y - a x i s on a suitable scale. We construct rectangles with class intervals as bases and the corresponding frequencies as heights. Thus, we obtain a histogram as shown below We have to find the mode of the following frequency distribution. Inside the highest rectangle corresponding to 57 (which represents the class with maximum frequency, i.e. modal class 49 . 5 - 59 . 5 ), we draw two straight lines from the corners of the rectangles on both sides of the highest rectangle to the opposite corners of the highest rectangle. Through the point of intersection P of the two straight lines drawn,we draw a vertical line to meet the X - axis at the point M (say). The variate at.the point M is the required mode. The mode is found at M ( 53 . 5 ). Hence, the required mode of the frequency distribution is 53 . 5 .

Draw a histogram for the distributions and estimate their modes. Marks % 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 90 - 99 Number of students 14 26 40 92 114 78 36

Given: The frequency distribution is Marks % 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 80 - 89 90 - 99 No. of students 14 26 40 92 114 78 36 We observe that, the given frequency distribution is not a continuous frequency distribution. In order to make it continuous, we subtract h 2 from the lower limit of each class and add h 2 to the upper limit of each class, where h = 40 - 39 = 1 Hence, the new frequency distribution is as follows: Marks % 29 . 5 - 39 . 5 39 . 5 - 49 . 5 49 . 5 - 59 . 5 59 . 5 - 69 . 5 69 . 5 - 79 . 5 79 . 5 - 89 . 5 89 . 5 - 99 . 5 No.of students 14 26 40 92 114 78 36 Next, we will construct a histogram with the modified frequency distribution table: Inside, the highest rectangle corresponding to the frequency 114 (which represents the class with maximum frequency, i.e. modal class 69 . 5 - 79 . 5 ), we draw two straight lines from the corners of the rectangles on both sides of the highest rectangle to the opposite corners of the highest rectangle. Through, the point of intersection P of the two straight lines drawn , we draw a vertical line to meet the X - axis at the point M (say). The variate at the point M is the required mode. The figure is as follows: The mode is obtained at M and the value is 73 . 5 .

Find the median for the following distribution graphically Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 7 10 8 5

Given: The frequency distribution is given as: The cumulative frequency table for the given continuous distribution is given below: Class -interval frequency Cumulative frequency 0 - 10 5 5 10 - 20 7 12 20 - 30 10 22 30 - 40 8 30 40 - 50 5 35 On the graph, we plot the following points: The required ogive is shown on the graph Next we will find the median: Here, total number of students = 35 Therefore, let P be the point on Y axis representing frequency n 2 = 35 2 = 17 . 5 Through P we draw a horizontal line to meet the ogive at point Q . Through Q , we draw a vertical line to meet the X -axis at T . The abscissa of the point T represents 26 . Hence, the median for the following distribution is 26 .

Estimate the median for the given data by drawing ogive. Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 frequency 4 9 15 14 8

Given: The frequency distribution is given as shown: The cumulative frequency table for the given continuous distribution is given below class frequency Cumulative frequency 0 - 10 4 4 10 - 20 9 13 20 - 30 15 28 30 - 40 14 42 40 - 50 8 50 Since, number of terms= 50 . Therefore, the median term will be 25 t h + 26 t h 2 t e r m = 25 . 5 t h t e r m On the graph, we plot the following terms: ( 10 , 4 ) , ( 20 , 13 ) , ( 30 , 28 ) , ( 40 , 42 ) a n d ( 50 , 50 ) The plot is as shown: To find the median: Let P be the point on Y-axis representing frequency n 2 = 50 2 = 25 Through P, we draw a horizontal line to meet the ogive at point Q. Through Q, we draw a vertical line to meet the X-axis at T. The abscissa of the point T represents 28 . Hence, the median is 28 . The required median is 28 .

MEDIUM

10th ICSE

IMPORTANT

Earn 100

Draw a histogram from the following frequency distribution and find the mode from the graph.

Class 0-5 5-10 10-15 15-20 20-25 25-30

frequency 2 5 18 14 8 5

Important Questions on Statistics

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 3

Find the mode of following data, using a histogram.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$12$	$20$	$9$	$4$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 4

The following table shows the expenditure of $60$ boys on books.

Expenditure (in ₹)	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
Number of Students	$4$	$7$	$23$	$18$	$6$	$2$

Find the mode of their expenditure.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 5

Using a graph paper draw a histogram for the given distribution showing the number of runs scored by $50$ batsman. Estimate the mode of the data.

Runs scored	Number of batsman
$3000 - 4000$	$4$
$4000 - 5000$	$18$
$5000 - 6000$	$9$
$6000 - 7000$	$6$
$7000 - 8000$	$7$
$8000 - 9000$	$2$
$9000 - 10000$	$4$

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 6

The marks of 200 students in a test are given below

Marks%	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$	$80 - 89$
Number of students	$7$	$11$	$20$	$46$	$57$	$37$	$15$	$7$

Draw the histogram and find the mode.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 7

Draw a histogram for the distributions and estimate their modes.

	Marks %	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$	$80 - 89$	$90 - 99$
	Number of students	$14$	$26$	$40$	$92$	$114$	$78$	$36$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 8

Find the mode of the following frequency distribution by drawing a histogram.

Mid values	$12$	$18$	$24$	$30$	$36$	$42$	$48$
frequency	$20$	$12$	$8$	$24$	$16$	$8$	$12$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 9

Find the median for the following distribution graphically

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$7$	$10$	$8$	$5$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 10

Estimate the median for the given data by drawing ogive.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
frequency	$4$	$9$	$15$	$14$	$8$

Draw a histogram from the following frequency distribution and find the mode from the graph. Class 0-5 5-10 10-15 15-20 20-25 25-30 frequency 2 5 18 14 8 5

Important Questions on Statistics

Learn and Prepare for any exam you want !

Draw a histogram from the following frequency distribution and find the mode from the graph.

Class 0-5 5-10 10-15 15-20 20-25 25-30

frequency 2 5 18 14 8 5