A Mathematics aptitude test of 50 students was recorded as follows : Marks 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of Students 4 8 14 19 5 Draw a histogram for the above data using a graph paper and locate the mode.

value of Q is the mode Q = 82 A histogram is a graphical display of data using bars of different heights. In a histogram, each bar groups numbers into ranges. Taller bars show that more data falls in that range. A histogram displays the shape and spread of continuous sample data.

Marks obtained by 200 students in an examination are given below: 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 11 10 20 28 37 40 29 14 6 Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine: The median marks.

Marks No. of students Cumulative frequency 0 - 10 5 5 10 - 20 11 16 20 - 30 10 26 30 - 40 20 46 40 - 50 28 74 50 - 60 37 11 60 - 70 40 151 70 - 80 29 180 80 - 90 14 194 90 - 100 6 200 Median = 200 2 = 100 th term marks = B = 57 marks he median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. ... If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.

Marks obtained by 200 students in an examination are given below: 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 11 10 20 28 37 40 29 14 6 Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine: The number of students who failed if minimum marks required to pass is 40 ?

Marks No. of students Cumulative frequency 0 - 10 5 5 10 - 20 11 16 20 - 30 10 26 30 - 40 20 46 40 - 50 28 74 50 - 60 37 11 60 - 70 40 151 70 - 80 29 180 80 - 90 14 194 90 - 100 6 200 No. of Student failed = 46 The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data. Marks 5 6 7 8 9 Number of Students 6 a 16 13 b If the mean of the distribution is 7 . 2 find a and b .

Marks Number of students fx 5 6 30 6 a 6 a 7 16 112 8 13 104 9 b 9 b Total ∑ f = 35 + a + b ∑ fx = 246 + 6 a + 9 b Mean = ∑ f x ∑ f 7 . 2 = 246 + 6 a + 9 b 35 + a + b 1 . 2 a - 1 . 8 b = - 6 . . . . . . ( i ) Total students = 6 + 9 + 16 + 13 + b 40 = 35 + a + b a + b = 5 . . . . . . ( ii ) Multiply equation (ii) by 1 . 8 and add to equation (i) 1 . 8 a 1 . 8 b = 9 1 . 2 a + 1 . 8 b = - 6 3 a = 3 3 a = 3 a = 1 substituting a = 1 in equation (ii) b = 4

Find the mode and the median of the following frequency distribution : x 10 11 12 13 14 15 f 1 4 7 5 9 3

Since 14 occurs the most number of times ( 9 times), mode of the distribution = 14 x f C . f . 10 1 1 11 4 5 12 7 12 13 9 17 14 9 26 15 3 29 N = 29 Median = N 2 = 29 2 = 14 . 5 So we know that 17 cumulative frequency is greater then 14 . 5 Hence median is 13 th

R K Bansal Solutions for Exercise 1: EXERCISE

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Attempt the practice questions from Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. Concise Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 11

The monthly income of a group of $320$ employees in a company is given below:

Monthly Income

[in thousands ]

6 - 7

7 - 8

8 - 9

9 - 10

10 - 11

11 - 12

12 - 13

No.of Employees

20

45

65

95

60

30

5

Draw an ogive of the given distribution on a graph sheet taking $2 cm = ₹ 1000$ on one axis and $2 cm = 50$ employees on the other axis. From the graph determine: The upper quartile.

EASY

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 12

A Mathematics aptitude test of $50$ students was recorded as follows :

Marks	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of Students	$4$	$8$	$14$	$19$	$5$

Draw a histogram for the above data using a graph paper and locate the mode.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 13

Marks obtained by $200$ students in an examination are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of students.	$5$	$11$	$10$	$20$	$28$	$37$	$40$	$29$	$14$	$6$

Draw an ogive for the given distribution taking $2 cm = 10$ marks on one axis and $2 cm = 20$ students on the other axis. Using the graph, determine:

The median marks.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 13

Marks obtained by $200$ students in an examination are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of students.	$5$	$11$	$10$	$20$	$28$	$37$	$40$	$29$	$14$	$6$

Draw an ogive for the given distribution taking $2 cm = 10$ marks on one axis and $2 cm = 20$ students on the other axis. Using the graph, determine:

The number of students who failed if minimum marks required to pass is $40$ ?

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 13

Marks obtained by $200$ students in an examination are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of students.	$5$	$11$	$10$	$20$	$28$	$37$	$40$	$29$	$14$	$6$

Draw an ogive for the given distribution taking $2 cm = 10$ marks on one axis and $2 cm = 20$ students on the other axis. Using the graph, determine:

If scoring $85$ and more marks is considered as grade one, find the number of students who secured grade one in the examination?

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 14

Marks obtained by $40$ students in a short assessment is given below, where $a$ and $b$ are two missing data.

Marks	$5$	$6$	$7$	$8$	$9$
Number of Students	$6$	$a$	$16$	$13$	$b$

If the mean of the distribution is $7.2$ find $a$ and $b$ .

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 15

Find the mode and the median of the following frequency distribution :

$x$	$10$	$11$	$12$	$13$	$14$	$15$
$f$	$1$	$4$	$7$	$5$	$9$	$3$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 16

The medain of the observations $11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47$ arranged in ascending order is $24$ . Find the value of $x$ and hence find the mean.

R K Bansal Solutions for Exercise 1: EXERCISE

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

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