Not the exact question you were looking for?

Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.

Statistics
NCERT Exemplar Ch 12
CBSE_NCERT_EXEMPLAR_CH12
Grade 10

Question:

If the median of the distribution given below is $28.5$, find the values of $x$ and $y$.
Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, Total
Frequency: 5, x, 20, 15, y, 5, 60

Step-by-Step Solution

Key Concept: Total frequency $N = 60 \Rightarrow 45 + x + y = 60 \Rightarrow x + y = 15$. Median is $28.5$, so median class is $20-30$ ($l=20, f=20, cf=5+x, h=10$). Apply median formula.
Stepwise Solution:

Total frequency: $5 + x + 20 + 15 + y + 5 = 60 \Rightarrow 45 + x + y = 60 \Rightarrow x + y = 15$ -- (eq 1). [1.0 Mark]

Given Median $= 28.5$, which lies in class $20-30$. So median class is $20-30$.
Here $l=20, f=20, cf = 5 + x, h=10, N/2 = 30$. [1.0 Mark]

$\text{Median} = l + \left(\dfrac{N/2 - cf}{f}\right)h \Rightarrow 28.5 = 20 + \left(\dfrac{30 - (5 + x)}{20}\right) \times 10$. [1.0 Mark]

$8.5 = \dfrac{25 - x}{2} \Rightarrow 17 = 25 - x \Rightarrow x = 8$. [1.0 Mark]

Substitute $x = 8$ into eq 1: $8 + y = 15 \Rightarrow y = 7$.
Values: $x = 8$ and $y = 7$. [1.0 Mark]

Marking Scheme:

• Equation $x + y = 15$: 1.0 Mark
• Identifying median class $20-30$ and parameters: 1.0 Mark
• Applying median formula $28.5 = 20 + (25-x)/2$: 1.0 Mark
• Solving for $x = 8$: 1.0 Mark
• Solving for $y = 7$: 1.0 Mark

Correct Answer:
Mathbee AI Mentor (Free Demo)

Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.

Master Statistics with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free