Median of Grouped Data

IMPORTANT

Median of Grouped Data: Overview

This Topic covers sub-topics such as Median, Median of Grouped Data, Median Class of Grouped Data, Relationship between Measures of Central Tendency and, Median as the Middle Most Observation in the Data

Important Questions on Median of Grouped Data

HARD

IMPORTANT

mathematics>Statistics>Median of Grouped Data> Q 1

If the median of the following frequency distribution is $46$ , then find the missing frequencies.

Class interval	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$12$	$30$	$?$	$65$	$?$	$25$	$18$	$230$

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mathematics>Statistics>Median of Grouped Data> Q 2

How do find median with cumulative frequency $?$

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mathematics>Statistics>Median of Grouped Data> Q 3

If the median of the following distribution is $58$ and sum of all the frequencies is $140$ . What is the value of $x and y$ ?

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

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mathematics>Statistics>Median of Grouped Data> Q 4

The heights of plants in Dipti's garden are recorded in the table given below. The median plant height is $55 cm$ .

Heights of plants (in $c m$ )	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Number of plants	$2 x$	$4$	$4 x$	$8$	$4$

The value of $x$ is?

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mathematics>Statistics>Median of Grouped Data> Q 5

Find out median of the following series:

Size	15	20	25	30	35	40
Frequency	10	15	25	5	5	20

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mathematics>Statistics>Median of Grouped Data> Q 6

The distribution below givens the weights of $30$ students of a class. Find the median weight of the students.

Weight $(in kg)$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$
Number of students	$2$	$3$	$8$	$6$	$6$	$3$	$2$

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mathematics>Statistics>Median of Grouped Data> Q 7

Let us find the median of the weight from the following frequency distribution table of $70$ students.

Weight $(kg)$	$43$	$44$	$45$	$46$	$47$	$48$	$49$	$50$
Number of students	$4$	$6$	$8$	$14$	$12$	$10$	$11$	$5$

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mathematics>Statistics>Median of Grouped Data> Q 8

Find the mode and median of the following data

C. I.	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency:	$6$	$10$	$12$	$8$	$7$

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mathematics>Statistics>Median of Grouped Data> Q 9

Find the mean using the formula $3 Median = Mode + 2 Mean$

Class Interval	Frequency
$1 - 5$	$7$
$5 - 9$	$2$
$9 - 13$	$2$
$13 - 17$	$8$
$17 - 21$	$1$

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mathematics>Statistics>Median of Grouped Data> Q 10

Explain applications of median in real life.

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mathematics>Statistics>Median of Grouped Data> Q 11

Find the median of the following distribution:

$x :$	$20$	$29$	$28$	$33$	$42$	$38$	$43$	$25$
$f :$	$6$	$28$	$24$	$15$	$2$	$4$	$1$	$20$

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mathematics>Statistics>Median of Grouped Data> Q 12

Find the median of the following distribution:

$x :$	$20$	$24$	$25$	$30$	$32$	$23$	$28$
$f :$	$10$	$11$	$15$	$12$	$15$	$14$	$13$

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mathematics>Statistics>Median of Grouped Data> Q 13

Find the median of the following distribution:

$x :$	$10$	$15$	$13$	$18$	$19$
$f :$	$6$	$8$	$12$	$15$	$10$

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mathematics>Statistics>Median of Grouped Data> Q 14

Calculate mode of the following $(6 - 7)$ by using empirical formula.

x	18	20	25	30	34	38	40
f	6	7	3	7	7	5	5

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mathematics>Statistics>Median of Grouped Data> Q 15

The percentage of marks obtained by 100 students in an examination are given below. Find median.

Marks	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$
Frequency	$10$	$16$	$18$	$23$	$18$	$8$	$7$

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mathematics>Statistics>Median of Grouped Data> Q 16

Find the median of the following distribution:

Height( $cm$ .)	$160 - 162$	$163 - 165$	$166 - 168$	$169 - 171$	$172 - 174$
Frequency	$15$	$117$	$136$	$118$	$14$

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mathematics>Statistics>Median of Grouped Data> Q 17

Find the values of frequencies $x$ and $y$ in the following frequency distribution table, if $N = 100$ and median is $32$ .

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
No. of students	$10$	$x$	$25$	$30$	$y$	$10$

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mathematics>Statistics>Median of Grouped Data> Q 18

Find the missing frequencies in the following frequency distribution table. if $N = 100$ and median is $32$ .

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	Total
Number of students	$10$	?	$25$	$30$	?	$10$	$100$

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mathematics>Statistics>Median of Grouped Data> Q 19

Find the median of the following data

$x_{i}$	$22$	$24.50$	$28$	$31.50$	$34$	$36.50$
$f_{i}$	$10$	$23$	$32$	$28$	$12$	$05$

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mathematics>Statistics>Median of Grouped Data> Q 20

Following is the distribution of the long jump competition in which $250$ students participated. Find the median distance jumped by the students. Interpret the median.

Distance	$0 - 1$	$1 - 2$	$2 - 3$	$3 - 4$	$4 - 5$
Number of students	$40$	$80$	$62$	$38$	$30$

Median of Grouped Data

Median of Grouped Data: Overview

Important Questions on Median of Grouped Data

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