Name: Relationship Between Mean, Median and Mode
Uploaded: 2019-07-19
Duration: 3 min 23 s
Description: The three main measures of central tendency, the mean, median and mode, are related to each other. Let's watch this video and learn about their relationship.

Question

The median of the following data is $525$ . Find the values of $x$ and $y$ , if the total frequency is $100$ .

Class Interval	Frequency
$0 - 100$	$2$
$100 - 200$	$5$
$200 - 300$	$x$
$300 - 400$	$12$
$400 - 500$	$17$
$500 - 600$	$20$
$600 - 700$	$y$
$700 - 800$	$9$
$800 - 900$	$7$
$900 - 1000$	$x$

Accepted Answer

Cumulative frequency for the given data;

Class interval Frequency $f$ Cumulative frequency CF

$0 - 100$ $2$ $2$

$100 - 200$ $5$ $7$

$200 - 300$ $x$ $x + 7$

$300 - 400$ $12$ $x + 19$

$400 - 500$ $17$ $600 - 700$

$500 - 600$ $20$ $9$

$600 - 700$ $y$ $x + y + 56$

$100$ $9$ $x + y + 65$

$2$ $7$ $x + y + 72$

$900 - 1000$ $4$ $x + y + 76$

total $Σ f = 76 + x + y = 100$

Given that the median is $600 - 700$ . So median class is $500 - 600$

Now median $= l + (\frac{\frac{N}{2} - C F}{f}) \times h$

where $l = 500, h = 100, N = 100, C F = 36 + x, f = 20$

so, $525 = 500 + (\frac{\frac{100}{2} - (36 + x)}{20}) \times 100$

$\Rightarrow 525 - 500 = (50 - (36 + x)) \times 5$

$\Rightarrow 25 = (14 - x) \times 5$

$\Rightarrow x = 9$

Also, $Σ f = 76 + x + y = 100$

$\Rightarrow 9 + y = 100 - 76$

$\Rightarrow y = 15$

Hence, $x = 9$ and $y = 15$

Age (in year)	$5 - 15$	$15 - 25$	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$
Number of patients	$6$	$11$	$21$	$23$	$14$	$5$

Class Interval	$10 - 25$	$25 - 40$	$40 - 55$	$55 - 75$	$70 - 85$	$85 - 100$
No. of students	$2$	$3$	$7$	$6$	$6$	$6$

Important Questions on Statistics

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

Important Questions on Statistics

Learn and Prepare for any exam you want !