If the mean of the following distribution is 3 , find the value of p . x i 1 2 3 5 p + 4 f i 9 6 9 3 6

x i f i f i x i 1 9 9 2 6 12 3 9 27 5 3 15 p + 4 6 6 p + 24 Σ f i = 33 Σf i x i = 6 p + 87 Mean x - = Σ f i x i Σ f i = 3 = 6 p + 87 33 ⇒ 99 = 6 p + 87 ⇒ 6 p = 12 ⇒ p = 2

Find the mode of the following frequency distribution: Class interval 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 Frequency 30 45 75 35 25 15

In the given frequency distribution class 20 - 25 has maximum frequency. So, 20 - 25 is the modal class Class interval Frequency 10 - 15 30 15 - 20 45 = f 0 20 - 25 75 = f 1 25 - 30 35 = f 2 30 - 35 25 35 - 40 15 Here, l = lower limit of the modal class = 20 , f 1 = frequency of modal class = 75 , f 0 = frequency of the class preceding the modal class = 45 , f 2 = frequency of the class succeeding the modal class = 35 , h = size of the modal class interval = 5 , Mode = l + f 1 - f 0 2 f 1 - f 0 - f 2 × h = 20 + 75 - 45 2 × 75 - 45 - 35 × 5 = 20 + 30 150 - 80 × 5 = 20 + 30 70 × 5 = 20 + 2 . 14 = 22 . 14 approx Hence, the mode is 22 . 14 .

Find the mode of the following frequency distribution: Age (in years) 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 Number of patients 6 11 18 24 17 13 5

In the given frequency distribution class 15 - 20 has maximum frequency. So, 15 - 20 is the modal class. Here, l = lower limit of the modal class = 15 , f 1 = frequency of modal class = 24 , f 0 = frequency of the class preceding the modal class = 18 , f 2 = frequency of the class succeeding the modal class = 17 , h = size of the modal class interval = 5 , Mode = l + f 1 - f 0 2 f 1 - f 0 - f 2 × h = 15 + 24 - 18 2 × 24 - 18 - 17 × 5 = 15 + 6 48 - 35 × 5 = 15 + 6 13 × 5 = 15 + 2 . 3 = 17 . 3 approx Hence, the mode is 17 . 3 years.

Find the mode of the following frequency distribution: Monthly salary (in ₹ ) 0 - 5000 5000 - 10000 10000 - 15000 15000 - 20000 20000 - 25000 25000 - 30000 Number of employees 90 150 100 80 70 10

In the given frequency distribution class 5000 - 10000 has maximum frequency. So, 5000 - 10000 is the modal class. Here, l = lower limit of the modal class = 5000 , f 1 = frequency of modal class = 150 , f 0 = frequency of the class preceding the modal class = 90 , f 2 = frequency of the class succeeding the modal class = 100 , h = size of the modal class interval = 5000 , Mode = l + f 1 - f 0 2 f 1 - f 0 - f 2 × h = 5000 + 150 - 90 2 × 150 - 90 - 100 × 5000 = 5000 + 60 300 - 190 × 5000 = 5000 + 60 110 × 5000 = 5000 + 2727 . 27 = 7727 . 27 approx Hence, the mode is ₹ 7727 . 27 .

Find out the mode of the following series: Wages ( ) Below 25 25 - 50 50 - 75 75 - 100 100 - 125 Above 125 No. of persons 10 30 40 25 20 15

Wages ( ) No. of persons ( f ) Below 25 10 25 - 50 30 f 0 50 - 75 40 f 1 75 - 100 25 f 2 100 - 125 20 Above 125 15 l = 50 , C = 25 Mode = l + f 1 - f 0 2 f 1 - f 0 - f 2 × C Mode = 50 + 40 - 30 ( 2 × 40 ) - 30 - 25 × 25 Mode = 50 + 10 25 × 25 Mode = 50 + 10 Mode = 60

E M B I B E

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 7

MEDIUM

10th Andhra Pradesh Board

IMPORTANT

Earn 100

Calculate the mean of the following distribution using Assumed Mean Method:

Class Interval $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$

Frequency $5$ $7$ $15$ $28$ $8$

Important Questions on Statistics

MEDIUM

10th Andhra Pradesh Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 8

If the mean of the following distribution is $3$ , find the value of $p$ .

$x_{i}$	$1$	$2$	$3$	$5$	$p + 4$
$f_{i}$	$9$	$6$	$9$	$3$	$6$

EASY

10th Andhra Pradesh Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 9

Find the mode of the following frequency distribution:

Class interval	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$
Frequency	$30$	$45$	$75$	$35$	$25$	$15$

EASY

10th Andhra Pradesh Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 10

Find the mode of the following frequency distribution:

Age (in years)	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Number of patients	$6$	$11$	$18$	$24$	$17$	$13$	$5$

EASY

10th Andhra Pradesh Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 11

Find the mode of the following frequency distribution:

Monthly salary (in $₹$ )	$0 - 5000$	$5000 - 10000$	$10000 - 15000$	$15000 - 20000$	$20000 - 25000$	$25000 - 30000$
Number of employees	$90$	$150$	$100$	$80$	$70$	$10$