Find the mode and the mean for the following data: Class 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 4 8 10 12 10 4 2

We know that in order to find the mode in a grouped frequency distribution, first, we have to find the modal class, which is the class with the maximum frequency. The mode is the value which lies inside the modal class and is given by the formula mode = l + f 1 - f 0 2 f 1 - f 0 - f 2 × h , where: l = lower limit of the modal class h = size of class (assuming that all classes have equal size) f 1 = frequency of the modal class f 0 = frequency of the class preceding the modal class f 2 = frequency of the class succeeding the modal class Let us look at the given table: Class 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 4 8 10 12 10 4 2 Clearly, the modal class is 40 - 50 . Here, l = 40 , h = 50 - 40 = 10 , f 1 = 12 , f 0 = 10 and f 2 = 10 . So, the mode = 40 + 12 - 10 2 × 12 - 10 - 10 × 10 = 40 + 2 4 × 10 = 40 + 5 = 45 So, the mode of the given data is 45 . Now, we shall compute the mean of the given data. We shall use the step deviation method. We shall take the assumed mean, a = 45 and class width, h = 10 (class width) and construct the table as under: Class Mid value x i Frequency f i d i = x i - 45 u i = d i h = x i - 45 10 f i u i 10 - 20 15 4 - 30 - 3 - 12 20 - 30 25 8 - 20 - 2 - 16 30 - 40 35 10 - 10 - 1 - 10 40 - 50 45 12 0 0 0 50 - 60 55 10 10 1 10 60 - 70 65 4 20 2 8 70 - 80 75 2 30 3 6 Total ∑ f i = 50 ∑ f i u i = - 14 Now, mean = a + h × ∑ f i u i ∑ f i = 45 + 10 - 14 50 = 45 - 2 . 8 = 42 . 2 Hence, the required mode of the given data is 45 and the mean of the given data is 42 . 2 .

M L Aggarwal Solutions for Chapter: Statistics, Exercise 2: Exercise 15.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 2: Exercise 15.2

Attempt the practice questions on Chapter 15: Statistics, Exercise 2: Exercise 15.2 with hints and solutions to strengthen your understanding. CBSE Syllabus Standard Mathematics for Class X solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 2: Exercise 15.2 with Hints & Solutions

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 4

Find the mode of the following frequency distribution:

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$8$	$10$	$10$	$16$	$12$	$6$	$7$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 5

The weight of coffee in $70$ packets is shown in the following table:

Weight (in $kg$ )	$200 - 201$	$201 - 202$	$202 - 203$	$203 - 204$	$204 - 205$	$205 - 206$
Number of packets	$12$	$26$	$20$	$9$	$2$	$1$

If the modal weight is $p kg$ , find $p$ .

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 6

Given below is the distribution of weekly pocket money received by students of a class. If the pocket money that is received by most of the students is $₹ k$ , find $k$ .

Pocket money (in $₹$ )	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Number of students	$2$	$2$	$3$	$12$	$18$	$5$	$2$

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 7

Find the mode (round-off up to two places after the decimal point) of the following frequency distribution:

Class	$45 - 50$	$40 - 45$	$35 - 40$	$30 - 35$	$25 - 30$	$20 - 25$	$15 - 20$
Frequency	$6$	$9$	$10$	$20$	$30$	$18$	$7$

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 8

Find the mode (up to two places after the decimal point) of the following frequency distribution:

Class	$16 - 20$	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$	$41 - 45$	$46 - 50$
Frequency	$2$	$11$	$26$	$35$	$22$	$19$	$5$

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 9

Find the mode and the mean for the following data:

Class	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$4$	$8$	$10$	$12$	$10$	$4$	$2$

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 10

Find the value of $f$ from the following data if its mode is $65$ :

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$
Frequency	$6$	$8$	$f$	$12$	$6$	$5$

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.2>Q 11

Mode of the following frequency distribution is $65$ and the sum of all the frequencies is $70$ . Find the missing frequencies $x$ and $y$ .

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$	$140 - 160$
Frequency	$8$	$11$	$x$	$12$	$y$	$9$	$9$	$5$

M L Aggarwal Solutions for Chapter: Statistics, Exercise 2: Exercise 15.2

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 2: Exercise 15.2

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 2: Exercise 15.2 with Hints & Solutions

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