Question

The first quartile of the given data is 35. find the value of x.
X 0-20/20-40/40-60/60-80/80-100
F 2 x 8 5 1​

Answer 1

The given value of the first quartile is related to the value cumulative

frequency up to the class of the first quartile.

• The value of x is 1

Reasons:

The first quartile is one of the five number summary.

The number of terms, N = 2 + x + 8 + 5 + 1 =16 + x

$\displaystyle Q_1 = \frac{N+1}{4} \ th \ value = \mathbf{\frac{17 + x}{4} \ th \ value}$

We have;

$\displaystyle Q_1 = \mathbf{ L + \frac{ \left (\frac{N + 1}{4} - pcf \right) }{f} \times C}$

Where;

The first quartile, Q₁ = 35

L = 20 in the first quartile class

PCF = The cumulative frequency of the first quartile class = 2 + x

f = The frequency of the quartile class = x

C = The class size = 10

Therefore;

$\displaystyle Q_1 = 35 = \mathbf{ 20 + \frac{ \left (\frac{17 + x}{4} - (2 + x) \right) }{x} \times 10}$

Which gives;

$\displaystyle 35 = \mathbf{\frac{25 \cdot x + 45}{2 \cdot x}}$

Therefore;

70·x = 25·x + 45

45·x = 45

x = 45 ÷ 45 = 1

• x = 1

Learn more about the five number summary here:

https://brainly.com/question/4530105