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 .

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

EASY

Earn 100

The number of members of $30$ families of a village is given in the following table. Find their Mode.

No. of members $2$ $3$ $4$ $5$ $6$ $7$ $8$

No. of families $1$ $2$ $4$ $6$ $10$ $3$ $5$

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Important Questions on Statistics

MEDIUM

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The table below shows the salaries of $280$ persons:

Salary(In thousand $₹$ )	Number of persons
$5 ‐ 10$	$49$
$10 ‐ 15$	$133$
$15 ‐ 20$	$63$
$20 ‐ 25$	$15$
$25 ‐ 30$	$6$
$30 ‐ 35$	$7$
$35 ‐ 40$	$4$
$40 ‐ 45$	$2$
$45 ‐ 50$	$1$

Calculate the median salary of the data in $₹$ , rounded off to the nearest whole number.

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

What is the mode of the following list of numbers :

$2$ , $4$ , $5$ , $6$ , $5$ , $4$ , $3$ , $5$ , $3$ , $1$ and $7$ ?

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

What is the mode of the given data?

$4, 3, 7, 13, 16, 23, 3, 4, 7, 4, 3, 3, 9, 6, 9, 6$

MEDIUM

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

Find the mean of the following distribution:

Class	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$
Frequency	$5$	$10$	$10$	$7$	$8$

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The following is the price of Cabbage over 12 months. What is the median price?

Question Image

MEDIUM

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

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	$f_{1}$	$5$	$9$	$12$	$f_{2}$	$3$	$2$	$40$

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The below graph shows the number of students Vs. Marks of students:

Question Image

In the given histogram, in which class interval, the median marks lies:

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The median of the first seven prime numbers, is ______.

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The scores obtained by a team in kabaddi series is as follows:

17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

. Find the mean score obtained by the team?

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

Find the difference of mean and Median value of

5, 8, 2, 6, 9, 15, 12, 18 o f t h e n u m b e r

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

If the mean of the first

n

natural numbers is

15

, then find

n

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

Find the mode of the following distribution:

Class:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency:	$6$	$8$	$10$	$12$	$6$	$5$	$3$

MEDIUM

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

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	$2$	$5$	$x$	$12$	$17$	$20$	$y$	$9$	$7$	$4$

MEDIUM

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The table given below shows the salaries of $280$ persons.

Salary $(in thiusand ₹)$	Number of persons
$5 - 10$	$49$
$10 - 15$	$133$
$15 - 20$	$63$
$20 - 25$	$15$
$25 - 30$	$6$
$30 - 35$	$7$
$35 - 40$	$4$
$40 - 45$	$2$
$45 - 50$	$1$

Calculate the median salary of data. (in ₹)

HARD

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The mean of the following distribution is $18$ . Find the frequency $f$ of the class $19 - 21$ .

Class	$11 - 13$	$13 - 15$	$15 - 17$	$17 - 19$	$19 - 21$	$21 - 23$	$23 - 25$
Frequency	$3$	$6$	$9$	$13$	$f$	$5$	$4$

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The median of the given data

\frac{1}{2}, \frac{2}{7}, \frac{3}{4}, \frac{1}{3}, \frac{5}{8}

is:

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

For the given data:

Class	Frequency
$160 - 170$	$20$
$170 - 180$	$110$
$180 - 190$	$130$
$190 - 200$	$80$
$200 - 210$	$60$

The median is _____.

EASY

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

What is the median of the following list of numbers?

$5, 3, 6, 9, 11, 19$ and $1$

MEDIUM

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

The mean and median of $7, 5, 5, 2, 7, 6, 5, 3, 7, 6$ is-

1. $5.3$ and $5$

2. $5$ and $5.5$

3. $5$ and $6$

4. $5.3$ and $5.5$

MEDIUM

Mathematics>Statistics and Probability>Statistics>Mode of Grouped Data

Find the mode of the following frequency distribution.

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

No. of members	$2$	$3$	$4$	$5$	$6$	$7$	$8$
No. of families	$1$	$2$	$4$	$6$	$10$	$3$	$5$

The number of members of 30 families of a village is given in the following table. Find their Mode. No. of members 2 3 4 5 6 7 8 No. of families 1 2 4 6 10 3 5

Important Questions on Statistics

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The number of members of $30$ families of a village is given in the following table. Find their Mode.

No. of members $2$ $3$ $4$ $5$ $6$ $7$ $8$

No. of families $1$ $2$ $4$ $6$ $10$ $3$ $5$