If the median of the following distribution is 58 and the sum of all the frequencies is 140 . Find the values of x and y . Variable 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85 85 - 95 Frequency 8 10 x 25 40 y 15 7

Given table is, Variable 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 75 - 85 85 - 95 Frequency 8 10 x 25 40 y 15 7 The median of the above frequency distribution is 58 and the sum of all the frequencies is 140 , then we have to find the missing frequencies x and y . We create a cumulative frequency distribution table, we get, Class interval Frequency Cumulative frequency 15 - 25 8 8 25 - 35 10 18 35 - 45 x 18 + x 45 - 55 25 43 + x 55 - 65 40 83 + x 65 - 75 y 83 + x + y 75 - 85 15 98 + x + y 85 - 95 7 105 + x + y Sum = 140 Here, n = 105 + x + y ⇒ n 2 = 105 + x + y 2 ⇒ 105 + x + y = 140 ............ i The sum of all the frequencies n = 140 . Since, the median is 58 . Therefore, the median class is 55 - 65 . (Since 58 lies between 55 - 65 ). Now, l = 55 , f = 40 , cf = 43 + x and h = 10 ∴ Median = l + n 2 - cf f × h 58 = 55 + 140 2 - 43 + x 40 × 10 58 - 55 10 = 70 - 43 - x 40 3 10 = 27 - x 40 3 1 = 27 - x 4 ⇒ 12 = 27 - x ⇒ x = 15 Put x = 15 in the equation i , we get, 105 + 15 + y = 140 ⇒ y = 20 Hence, the values of x and y are 15 and 20 .

Draw a histogram from the following frequency distribution and find the mode from the graph. Class 0-5 5-10 10-15 15-20 20-25 25-30 frequency 2 5 18 14 8 5

Given:- The frequency distribution is:- Class 0-5 5-10 10-15 15-20 20-25 25-30 frequency 2 5 18 14 8 5 We represent the class intervals along the X - axis on a suitable scale and the corresponding frequencies along the Y - axis on a suitable scale. We construct rectangles with class intervals as bases and the corresponding frequencies as heights. Thus, we obtain a histogram as shown below Now, to find the mode, we draw two straight lines AC and BD in the highest rectangle, which intersect at P . Through point P , we draw a vertical line to meet the X - axis at N . It is shown as:- Therefore, the mode is at the point N and the corresponding value is 14 .

Find the mode of following data, using a histogram. Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 12 20 9 4

Given frequency distribution is:- Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 12 20 9 4 To create a histogram, first we represent the class intervals along the X - axis on a suitable scale and the corresponding frequencies along the Y - axis on a suitable scale. We construct rectangles with class intervals as bases and the corresponding frequencies as heights. Thus, we obtain a histogram as shown below: The process of finding the mode involves few steps: Inside the highest rectangle corresponding to 20 (which represents the modal class 20 - 30 ,we draw two straight lines from the corners of the rectangles on both sides of the highest rectangle to the opposite corners of the highest rectangle. Through, the point of intersection P of the two straight lines drawn in previous step, we draw a vertical line to meet the X - axis at the point M . The x -coordinate at point M is the required mode. Thus, From the histogram, we see that the mode is 24 .

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The weights $(in kg)$ of $45$ students of a class are given in the following distribution table. Determine the value of weight $x (kg)$ which is such that the number of students having weight less than $x kg$ is same as the number of students having weight more than $x kg$ .

Weight $(in kg)$ Cumulative frequency

Below $45$ $5$

Below $50$ $11$

Below $55$ $15$

Below $60$ $22$

Below $65$ $38$

Below $70$ $45$

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Important Questions on Statistics

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 10

Compute the median marks for the following data.

Marks	Number of students
$0$ and above	$50$
$10$ and above	$46$
$20$ and above	$40$
$30$ and above	$20$
$40$ and above	$10$
$50$ and above	$3$
$60$ and above	$0$

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10th ICSE

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All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 11

If the median of the following frequency distribution is $24$ , then find the missing frequency $x$ .

Age (in years)	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Number of persons	$5$	$25$	$x$	$18$	$7$

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 12

If the median of the following frequency distribution is $35$ , then find the value of $x$ .

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$2$	$3$	$x$	$6$	$5$	$3$	$2$

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 13

If the median of the following distribution is $58$ and the sum of all the frequencies is $140$ . Find the values of $x$ and $y$ .

Variable	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$	$75 - 85$	$85 - 95$
Frequency	$8$	$10$	$x$	$25$	$40$	$y$	$15$	$7$

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 14

If the median of the number of patients attending a hospital is $36$ , then find the missing frequencies $f_{1}$ and $f_{2}$ in the following frequency distribution, when it is given that the total number of days is $100$ .

Number of patients	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of days	$5$	$12$	$f_{1}$	$f_{2}$	$15$	$11$	$14$

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 15

During Medical check-up of $200$ students of the school, their weights were recorded as follows:-

Weight $(in kg)$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$	$80 - 89$
Number of students	$5$	$22$	$63$	$74$	$30$	$6$

Find the median weight $(kg)$ of students.

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 2

Draw a histogram from the following frequency distribution and find the mode from the graph.

Class	0-5	5-10	10-15	15-20	20-25	25-30
frequency	2	5	18	14	8	5

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 3

Find the mode of following data, using a histogram.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$12$	$20$	$9$	$4$

Weight $(in kg)$	Cumulative frequency
Below $45$	$5$
Below $50$	$11$
Below $55$	$15$
Below $60$	$22$
Below $65$	$38$
Below $70$	$45$

Important Questions on Statistics

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