The following table gives marks obtained (out of 25 ) by 71 students of Class X : Marks obtained 20 15 17 23 22 25 No. of students 15 7 10 9 17 13 Find the median marks obtained.

Marks Number of students C.F. 15 7 7 17 10 17 20 15 32 22 17 49 25 13 62 30 9 71 Now, number of students = 71 Which is odd. Then, median = n + 1 2 t h = 71 + 1 2 t h = 72 2 t h = 36 th term = 22

Fifty students recorded how much they spent on eating out in one month (to the nearest dollar). The results are shown in the partially complete frequency table: Class interval Class boundaries Frequency 1 - 10 0 . 5 - 10 . 5 14 11 - 20 10 . 5 - 20 . 5 13 21 - 30 15 31 - 40 0 41 - 50 4 51 - 60 3 61 - 70 1 State the class that contains the median.

The given table shows the amount spent on eating out in one month by students The table of given data Class interval Frequency cumulative frequency 1 - 10 14 14 11 - 20 13 27 21 - 30 15 42 31 - 40 0 42 41 - 50 4 46 51 - 60 3 49 61 - 70 1 50 Now, let n = sum of all frequencies n = 14 + 13 + 15 + 0 + 4 + 3 + 1 = 50 as n is even, so the position of median is the class whose cumulative frequency is greater than n 2 lies. Therefore, the position of median is the class whose cumulative frequency is greater than 50 2 = 25 So, this will be possible in 11 - 20 interval. So, the median will be in the interval 11 - 20 .

Fifty students recorded how much they spent on eating out in one month (to the nearest dollar). The results are shown in the partially complete frequency table: Class interval Class boundaries Frequency 1 - 10 0 . 5 - 10 . 5 14 11 - 20 10 . 5 - 20 . 5 13 21 - 30 15 31 - 40 0 41 - 50 4 51 - 60 3 61 - 70 1 State the modal class.

The given table shows the amount spent on eating out in one month by students The modal class is the class interval with the highest frequency. So, here we have highest frequency of 15 in class 21 - 30 So, 21 - 30 is the modal class of given data

A taxi driver records the distances of his journeys, to the nearest km, over the course of a long weekend shift. Distance 1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 Frequency 10 6 8 5 2 Write down the modal class.

Given frequency table is Distance 1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 Frequency 10 6 8 5 2 The modal class is the class interval with the highest frequency. So, here we have highest frequency of 10 in class 1 - 5 . So, 1 - 5 is the modal class of given data

The number of books in different shelves of a library are as follows: 30 , 32 , 28 , 24 , 20 , 25 , 38 , 37 , 40 , 45 , 16 , 20 19 , 24 , 27 , 30 , 32 , 34 , 35 , 42 , 27 , 28 , 19 , 34 , 38 , 39 , 42 , 29 , 24 , 27 , 22 , 29 , 31 , 19 , 27 , 25 28 , 23 , 24 , 32 , 34 , 18 , 27 , 25 , 37 , 31 , 24 , 23 43 , 32 , 28 , 31 , 24 , 23 , 26 , 36 , 32 , 29 , 28 , 21 Prepare a cumulative frequency distribution table using 45 - 49 as the last class interval.

The minimum and maximum numbers of books in shelves are 16 and 45 . The range is 45 - 16 = 29 Given that 45 - 49 is the last class-interval. So, the class size is 49 - 45 = 4 Now calculate Range Class - size = 29 4 = 7 . 25 Thus, the number of classes is 8 . The cumulative frequency distribution is the following: No.of Books No.of Shohes (Frequency) Cumulative Frequency 13 - 17 1 1 17 - 21 6 7 21 - 25 11 18 25 - 29 15 33 29 - 33 12 45 33 - 37 5 50 37 - 41 6 56 41 - 45 3 59 45 - 49 1 60

The median of the following data is 525 . Find the values of x and y , if total frequency is 100 . Class 0 - 100 100 - 200 200 - 300 300 - 400 400 - 500 500 - 600 600 - 700 700 - 800 800 - 900 900 - 1000 Frequency 2 5 x 12 17 20 y 9 7 4

Cumulative frequency for the given data; Class interval Frequency f Cumulative frequency CF 0 - 100 2 2 100 - 200 5 7 200 - 300 x x + 7 300 - 400 12 x + 19 400 - 500 17 x + 36 500 - 600 20 x + 56 600 - 700 y x + y + 56 700 - 800 9 x + y + 65 800 - 900 7 x + y + 72 900 - 1000 4 x + y + 76 total Σ f = 76 + x + y = 100 Given that the median is 525 . So median class is 500 - 600 Now median = l + N 2 - C F f × h where l = 500 , h = 100 , N = 100 , C F = 36 + x , f = 20 so, 525 = 500 + 100 2 - ( 36 + x ) 20 × 100 ⇒ 525 - 500 = ( 50 - ( 36 + x ) ) × 5 ⇒ 25 = ( 14 - x ) × 5 ⇒ x = 9 Also, Σ f = 76 + x + y = 100 ⇒ 9 + y = 100 - 76 ⇒ y = 15 Hence, x = 9 and y = 15

If the median of the following frequency distribution is 32 . 5 . Find the values of f 1 and f 2 . Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency f 1 5 9 12 f 2 3 2 40

Find the Cumulative Frequency of the given data. class Frequency f Cumulative Frequency c f 0 - 10 f 1 f 1 10 - 20 5 f 1 + 5 20 - 30 9 f 1 + 14 30 - 40 12 f 1 + 26 40 - 50 f 2 f 1 + f 2 + 26 50 - 60 3 f 1 + f 2 + 29 60 - 70 2 f 1 + f 2 + 31 N = ∑ f = 40 Sum of Cumulative Frequency is f 1 + f 2 + 31 = 40 ⇒ f 1 + f 2 = 9 . . . . . . . ( 1 ) Now, The median 32 . 5 is lies between 30 - 40 . Hence, median class is 30 - 40 . ∴ l = 30 , N 2 = 40 2 = 20 , h = 10 , f = 12 , cumulative frequency of preceding class ( cf ) = 14 + f 1 . Now, median is given as, M = l + ( N 2 - cf ) f × h 32 . 5 = 30 + ( 20 - ( 14 + f 1 ) 12 × 10 2 . 5 = ( 60 - 10 f 1 ) 12 30 = 60 - 10 f 1 f 1 = 30 10 f 1 = 3 From equation ( 1 ) , we get f 2 = 9 - f 1 f 2 = 9 - 3 f 2 = 6 Hence, the value of f 1 is 3 and f 2 is 6 .

EASY

10th Rajasthan Board

IMPORTANT

Earn 100

The height of students in a class is given below:

Create a frequency distribution table with class interval of $5 cm$

$150, 151, 152, 155, 164, 166, 155, 156, 151, 151, 157, 159, 161, 168, 169, 162, 163, 157, 154,$

Important Questions on Statistics

HARD

10th Rajasthan Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 5

The following table gives marks obtained (out of $25$ ) by $71$ students of Class $X$ :

Marks obtained	$20$	$15$	$17$	$23$	$22$	$25$
No. of students	$15$	$7$	$10$	$9$	$17$	$13$

Find the median marks obtained.

EASY

10th Rajasthan Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 6

Fifty students recorded how much they spent on eating out in one month (to the nearest dollar). The results are shown in the partially complete frequency table:

Class interval	Class boundaries	Frequency
$1 - 10$	$0.5 - 10.5$	$14$
$11 - 20$	$10.5 - 20.5$	$13$
$21 - 30$		$15$
$31 - 40$		$0$
$41 - 50$		$4$
$51 - 60$		$3$
$61 - 70$		$1$

State the class that contains the median.

EASY

10th Rajasthan Board

IMPORTANT

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

Fifty students recorded how much they spent on eating out in one month (to the nearest dollar). The results are shown in the partially complete frequency table:

Class interval	Class boundaries	Frequency
$1 - 10$	$0.5 - 10.5$	$14$
$11 - 20$	$10.5 - 20.5$	$13$
$21 - 30$		$15$
$31 - 40$		$0$
$41 - 50$		$4$
$51 - 60$		$3$
$61 - 70$		$1$

State the modal class.

EASY

10th Rajasthan Board

IMPORTANT

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

A taxi driver records the distances of his journeys, to the nearest km, over the course of a long weekend shift.

Distance	$1 - 5$	$6 - 10$	$11 - 15$	$16 - 20$	$21 - 25$
Frequency	$10$	$6$	$8$	$5$	$2$

Write down the modal class.

HARD

10th Rajasthan Board

IMPORTANT

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

Find the missing frequencies in the following distribution table. It is given that the mean of these distributions is

56

and their total is

90 i . e . \sum f = 90 .

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$
Frequency	$16$	$f_{1}$	$25$	$f_{2}$	$12$	$10$

HARD

10th Rajasthan Board

IMPORTANT

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

The number of books in different shelves of a library are as follows:

$\begin{array}{l} 30, 32, 28, 24, 20, 25, 38, 37, 40, 45, 16, 20 \\ 19, 24, 27, 30, 32, 34, 35, 42, 27, 28, 19, 34, \\ 38, 39, 42, 29, 24, 27, 22, 29, 31, 19, 27, 25 \end{array} \begin{array}{l} 28, 23, 24, 32, 34, 18, 27, 25, 37, 31, 24, 23 \\ 43, 32, 28, 31, 24, 23, 26, 36, 32, 29, 28, 21 \end{array}$

Prepare a cumulative frequency distribution table using $45 - 49$ as the last class interval.

MEDIUM

10th Rajasthan Board

IMPORTANT

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

Your tutor says that your test scores in Physics are better than your test scores in Chemistry. Your results (out of $100$ ) for the last six tests in each subject are presented in this table:

Chemistry	$56$	$64$	$66$	$58$	$72$	$81$
Physics	$64$	$62$	$72$	$73$	$60$	$70$

Comment on your tutor's claim.

MEDIUM

10th Rajasthan Board

IMPORTANT

Mathematics Crash Course (Based on Revised Syllabus-2023)>Chapter 14 - Statistics>Exercise>Q 12

You suspect that boys are spending more money than girls in your school canteen. You stand by the cashier one lunch time and record the amount spent by the first ten girls and by the first ten boys. The amounts you record are as follows:

Boys		Girls
$$ 3.12$	$$ 1.00$	$$ 4.00$	$$ 2.51$
$$ 4.00$	$$ 6.37$	$$ 1.37$	$$ 0.88$
$$ 4.00$	$$ 4.00$	$$ 4.00$	$$ 4.00$
$$ 5.16$	$$ 3.82$	$$ 4.00$	$$ 4.80$
$$ 2.13$	$$ 3.65$	$$ 2.32$	$$ 3.55$

Comment on the claim that boys spend more than girls in the canteen.

The height of students in a class is given below: Create a frequency distribution table with class interval of 5 cm 150,151,152,155,164,166,155,156,151,151,157,159,161,168,169,162,163,157,154,

Important Questions on Statistics

Learn and Prepare for any exam you want !

The height of students in a class is given below:

Create a frequency distribution table with class interval of $5 cm$

$150, 151, 152, 155, 164, 166, 155, 156, 151, 151, 157, 159, 161, 168, 169, 162, 163, 157, 154,$