Question

The median of the following data is 167. Find the values of x.
Height(in cm) 160-162 163-165 166-168 169-171 172-174
Frequency 15 117 x 118 14

Answer 1

Answer:

2.79 is the required value of x .

Step-by-step explanation:

Explanation:

Given, class interval :160-162,163-165,166-168,169-171,172-174

Frequency : 15, 117, x,118 ,14

Median = 167

Here we see that median is 167 , which is lies in 166-168 class interval .

Median = $l + (\frac{\frac{n}{2}- c.f }{f} )h$

L = lower limit  of class median

h = difference between two consecutive class interval

f = highest frequency .

Step 1:

Therefore ,  l = 166 , h = 2  and c.f = 132+x

f   = 118   (highest frequency )

n = 264+x ⇒ $\frac{n}{2} = \frac{264+x}{2}$ .

Formula of median = $l + (\frac{\frac{n}{2}- c.f }{f} )h$

⇒167 = $166 +(\frac{\frac{264+x}{2} -(132+x)}{118} )2$

⇒ 167 = 166 - $\frac{59x}{2}$

⇒167= 332 - 59x

⇒59x = 332- 167 = 165

⇒$x = \frac{165}{59} = 2.79$

Final answer :

Hence , the value of x is 2.79