Draw a histogram for the following frequency distribution. Use of electricity (Unit) 50 - 70 70 - 90 90 - 110 110 - 130 130 - 150 150 - 170 Number of families 150 400 460 540 600 350

We need to draw a histogram for the following data. Use of electricity (Unit) 50 - 70 70 - 90 90 - 110 110 - 130 130 - 150 150 - 170 Number of families 150 400 460 540 600 350 For the histogram, We can take the use of electricity(units) on the x -axis and the number of families on the y -axis. Taking each class as the base, we need to draw rectangles with heights proportional to the frequencies. So, the required histogram is shown below.

Draw a frequency polygon for the following grouped frequency distribution table. Age of the donor (Years) 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 Number of blood donors 38 46 35 24 15 12

For a given frequency distribution table, A frequency polygon is plotted using the class mark of the given classes and the corresponding frequency as the coordinates. We know that, Class mark is the average of upper and lower limits of the respective class interval. And, to make a given frequency distribution table continuous, we can add 0 . 5 to the upper limit of the class intervals and subtract 0 . 5 from the lower limit of the class intervals. So, we can rewrite the given frequency distribution table. The given class interval (Age of the donor) Continuous class interval Class mark Frequency (Number of blood donors) 20 - 24 19 . 5 - 24 . 5 22 38 25 - 29 24 . 5 - 29 . 5 27 46 30 - 34 29 . 5 - 34 . 5 32 35 35 - 39 34 . 5 - 39 . 5 37 24 40 - 44 39 . 5 - 44 . 5 42 15 45 - 49 44 . 5 - 49 . 5 47 12 With the above coordinates, we can plot the required frequency polygon.

The following table shows the average rainfall in 150 towns. Show the information by a frequency polygon. Average rainfall ( cm ) 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 Number of towns 14 12 36 48 40

For a given frequency distribution table, A frequency polygon is plotted using the class mark of the given classes and the corresponding frequency as the coordinates. We know that, Class mark is the average of upper and lower limits of the respective class interval. So, we can rewrite the given table by making the class intervals continuous. Class interval (Average rainfall in cm ) Class mark Frequency (Number of towns) 0 - 20 10 14 20 - 40 30 12 40 - 60 50 36 60 - 80 70 48 80 - 100 90 40 With the above coordinates, we can plot the required frequency polygon.

Maharashtra Board Solutions for Chapter: Statistics, Exercise 1: Miscellaneous Problems

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Statistics, Exercise 1: Miscellaneous Problems

Attempt the practice questions on Chapter 7: Statistics, Exercise 1: Miscellaneous Problems with hints and solutions to strengthen your understanding. Algebra Standard X solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Statistics, Exercise 1: Miscellaneous Problems with Hints & Solutions

EASY

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 1

The formula to find mean from a grouped frequency table is $\bar{x} = A + \frac{\sum f_{i} u_{i}}{\sum f_{i}} \times h g$ . In the formula, $u_{i} =$

MEDIUM

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 1

Distance covered per litre ( $km$ )	$12 - 14$	$14 - 16$	$16 - 18$	$18 - 20$
Number of cars	$11$	$12$	$20$	$7$

The median of the distances covered per litre shown in the above data is in the group

MEDIUM

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 1

Number of trees planted by each student	$1 - 3$	$4 - 6$	$7 - 9$	$10 - 12$
Number of students	$7$	$8$	$6$	$4$

If the above data is to be shown by a frequency polygon, then the coordinates of the point to show the number of students in the class $4 - 6$ is

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 9

Draw a histogram for the following frequency distribution.

Use of electricity (Unit)	$50 - 70$	$70 - 90$	$90 - 110$	$110 - 130$	$130 - 150$	$150 - 170$
Number of families	$150$	$400$	$460$	$540$	$600$	$350$

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 10

In a hand loom factory, different workers take different periods of time to weave a saree. The number of workers and their required periods are given below. Present the information by a frequency polygon.

Number of days	$8 - 10$	$10 - 12$	$12 - 14$	$14 - 16$	$16 - 18$	$18 - 20$
Number of workers	$5$	$16$	$30$	$40$	$35$	$14$

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 11

The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon.

Time required for experiment (minutes)	$20 - 22$	$22 - 24$	$24 - 26$	$26 - 28$	$28 - 30$	$30 - 32$
Number of students	$8$	$16$	$22$	$18$	$14$	$12$

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 12

Draw a frequency polygon for the following grouped frequency distribution table.

Age of the donor (Years)	$20 - 24$	$25 - 29$	$30 - 34$	$35 - 39$	$40 - 44$	$45 - 49$
Number of blood donors	$38$	$46$	$35$	$24$	$15$	$12$

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 6 - Statistics>Miscellaneous Problems>Q 13

The following table shows the average rainfall in $150$ towns. Show the information by a frequency polygon.

Average rainfall ( $cm$ )	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Number of towns	$14$	$12$	$36$	$48$	$40$

Maharashtra Board Solutions for Chapter: Statistics, Exercise 1: Miscellaneous Problems

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Statistics, Exercise 1: Miscellaneous Problems

Questions from Maharashtra Board Solutions for Chapter: Statistics, Exercise 1: Miscellaneous Problems with Hints & Solutions

Learn and Prepare for any exam you want !