General Test>Quantitative Reasoning>Measures of Central Tendency and Dispersion>Median

Median

IMPORTANT

Median: Overview

This topic covers concepts, such as Understanding Applications of Measures of Central Tendency, Median as the Middle Most Observation in the Data, Median for Odd Number of Data, Relationship Median of Grouped Data, Median, etc.

Important Questions on Median

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 1

Find the median for the given grouped data.

$x$	$50 - 75$	$75 - 100$	$100 - 125$	$125 - 150$	$150 - 175$
$f$	$425$	$625$	$a$	$614$	$320$

Where,

$a$ , is the mode for the continuous data given below.

Class	$50 - 150$	$150 - 250$	$250 - 350$	$350 - 450$	$450 - 550$
Number of people	$50$	$40$	$30$	$100$	$60$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 2

Find the median for the given grouped data.

$x$	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$
$f$	$300$	$a$	$328$	$426$	$320$

Where,

$a$ , is the approximate value of the mode value for the continuous data given below.

Class	$50 - 100$	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$
Number of people	$25$	$50$	$75$	$100$	$125$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 3

Find the median for the given grouped data.

$x$	$10 - 30$	$30 - 50$	$50 - 70$	$70 - 90$	$90 - 110$
$f$	$400$	$420$	$a$	$320$	$100$

Where,

$a$ , is the approximate value of the mode value for the continuous data given below.

Class	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$	$500 - 600$
Number of people	$15$	$30$	$45$	$60$	$75$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 4

Find the median for the given grouped data.

$x$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
$f$	$10$	$a + 5$	$2 a$	$a + 5$	$10$

Where,

$a$ , is the median for the grouped data given below.

$x$	$11$	$13$	$15$	$17$	$19$
$f$	$15$	$20$	$25$	$20$	$15$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 5

Find the median for the given grouped data.

$x$	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$
$f$	$5$	$7$	$a + 1$	$2 a$	$4 a$

Where,

$a$ , is the median for the grouped data given below.

$x$	$3$	$5$	$7$	$9$	$11$
$f$	$15$	$25$	$35$	$45$	$55$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 6

Find the median for the given grouped data.

$x$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
$f$	$15$	$a$	$a + 10$	$25$	$a + 15$

Where,

$a$ , is the median for the grouped data given below.

$x$	$10$	$15$	$20$	$25$	$30$
$f$	$15$	$30$	$21$	$23$	$19$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 7

Find the median for the given grouped frequency distribution.

$x$	$12$	$24$	$36$	$42$	$63$
$f$	$a$	$14$	$a$	$16$	$a + 6$

Where,

$a$ , is the median of the ungrouped data shown below.

$5, 7, 6, 8, 10, 8, 11, 12, 17, 15, 19, 22, 21, 25, 23$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 8

Find the median for the given grouped frequency distribution.

$x$	$20$	$21$	$23$	$25$	$27$
$f$	$15$	$17$	$a$	$18$	$21$

Where,

$a$ , is the median of the ungrouped data shown below.

$8, 7, 9, 12, 10, 13, 14, 17, 15, 18, 22, 20, 24, 29, 27, 26$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 9

Find the median for the given grouped frequency distribution.

$x$	$21$	$23$	$25$	$26$	$29$
$f$	$15$	$14$	$a$	$22$	$33$

Where,

$a$ , is the median of the ungrouped data shown below.

$6, 8, 7, 9, 15, 13, 11, 19, 17, 25, 30, 26$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 10

Find the median for the given grouped frequency distribution.

$x$	$21$	$23$	$25$	$26$	$29$
$f$	$150$	$147$	$a$	$225$	$325$

Where,

$a,$ is the mean for the continuous data given below

Class	$50 - 100$	$100 - 150$	$150 - 200$	$200 - 250$
Number of people	$100$	$200$	$300$	$400$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 11

Find the median for the given grouped frequency distribution.

$x$	$11$	$12$	$13$	$14$	$15$
$f$	$410$	$441$	$a$	$440$	$331$

Where,

$a,$ is the mean value for the continuous data given below.

Class	$310 - 390$	$390 - 510$	$510 - 590$	$590 - 710$
Number of people	$350$	$250$	$350$	$450$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 12

Find the median for the given grouped frequency distribution.

$x$	$20$	$40$	$60$	$80$	$100$
$f$	$310$	$330$	$a$	$370$	$400$

Where,

$a,$ is the mean for the continuous data given below

Class	$510 - 590$	$590 - 710$	$710 - 790$	$790 - 910$
Number of people	$250$	$350$	$150$	$250$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 13

In the following question given below, on solving the given statement, we get quantities $I$ and $II$ , solve both quantities and choose the correct option.

Quantity $I :$ Find the median for the given grouped frequency distribution.

$x$	$2$	$4$	$6$	$8$	$10$
$f$	$31$	$33$	$35$	$37$	$40$

Quantity $II :$ Find the median for the given grouped frequency distribution.

$x$	$3$	$5$	$7$	$9$	$11$
$f$	$41$	$43$	$45$	$47$	$50$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 14

In the following question given below, on solving the given statement, we get quantities $I$ and $II$ , solve both quantities and choose the correct option.

Quantity $I :$ Find the median for the given grouped frequency distribution.

$x$	$11$	$12$	$13$	$14$	$15$
$f$	$42$	$52$	$57$	$63$	$30$

Quantity $II :$ Find the median for the given grouped frequency distribution.

$x$	$6$	$7$	$13$	$14$	$21$
$f$	$24$	$15$	$27$	$23$	$59$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 15

In the following question given below, on solving the given statement, we get quantities $I$ and $II$ , solve both quantities and choose the correct option.

Quantity $I :$ Find the median for the given grouped frequency distribution.

$x$	$10$	$20$	$30$	$40$	$50$
$f$	$100$	$150$	$175$	$200$	$225$

Quantity $II :$ Find the median for the given grouped frequency distribution.

$x$	$50$	$40$	$30$	$20$	$10$
$f$	$145$	$130$	$135$	$120$	$110$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 16

Find the median of the ungrouped data shown below.

$8, 9, 13, 10, 15, 19, 17, 20, 22, 21, 25, 23$

MEDIUM

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 17

Find the median of the ungrouped data shown below.

$10, 13, 11, 15, 17, 16, 19, 21, 20, 22, 25, 23, 26$

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 18

For the following ungrouped data:

$15, 18, 17, x, 18, x + 1, 21, x + 1, 24, 22, 26$

If the mean of the above-ungrouped data is $20$ , then find the median for the ungrouped data.

(Note: $x$ is less than $21$ but more than $18$ )

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 19

For the following ungrouped data:

$15, 8, 8, 6, x, x + 1, 13, 11, 15, 5$

If the mean of the above-ungrouped data is $10$ , then find the median for the ungrouped data.

(Note: $x$ is less than $11$ but more than $8$ )

HARD

IMPORTANT

General Test>Measures of Central Tendency and Dispersion>Median> Q 20

For the following ungrouped data:

$10, 13, 11, x, 14, x, x + 1, 17, 18$

If the mean of the above-ungrouped data is $14 \frac{1}{3}$ , then find the median for the ungrouped data.

(Note: $x$ is less than $17$ but greater than $14$ )