Master Statistics in 30 Minutes: A Quick Guide for CBSE Class 10 Students

Q&A Style Revision

1. What is the formula for calculating the Mean (Direct Method)?

The formula is:
Mean ((bar{x})) = (frac{sum f_i x_i}{sum f_i})

2. How do you calculate the Mean using the Assumed Mean Method?

The formula is:
(bar{x} = A + frac{sum f_i d_i}{sum f_i}), where (d_i = x_i – A).

3. What is the formula for Median of grouped data?

The formula is:
Median = (l + left(frac{frac{N}{2} – text{CF}}{f}right) times h)

Where:

• (l): Lower boundary of the median class
• (N): Total frequency ((sum f_i))
• (text{CF}): Cumulative frequency of the class preceding the median class
• (f): Frequency of the median class
• (h): Class width

4. How is Mode calculated for grouped data?

The formula is:
Mode = (l + left(frac{f_1 – f_0}{2f_1 – f_0 – f_2}right) times h)

Where:

• (f_1): Frequency of the modal class
• (f_0): Frequency of the class before the modal class
• (f_2): Frequency of the class after the modal class
• (h): Class width

5. How do you solve the given problem to calculate the Mean using the Assumed Mean Method?

Class Intervals: 0-10, 10-20, 20-30, 30-40

Frequency: 5, 8, 15, 12

Assumed Mean: (A = 25)

Solution:

1. Calculate midpoints (x_i) for each class: 5, 15, 25, 35.
2. Find (d_i = x_i – A): -20, -10, 0, 10.
3. Multiply (f_i) and (d_i): -100, -80, 0, 120.
4. Sum (f_i): 40. Sum (f_i d_i): -60.
5. Use formula: (bar{x} = A + frac{sum f_i d_i}{sum f_i} = 25 + frac{-60}{40} = 23.5).

Mean: 23.5

6. How do you find the Median for the given data?

Class Intervals: 0-10, 10-20, 20-30, 30-40

Frequency: 5, 8, 15, 12

Total Frequency ((N)): 40

Median Class: 20-30

Solution:

1. (l = 20, h = 10, text{CF} = 13, f = 15, N = 40).
2. Use formula: (text{Median} = l + left(frac{frac{N}{2} – text{CF}}{f}right) times h).
3. (text{Median} = 20 + left(frac{20 – 13}{15}right) times 10 = 20 + 4.67 = 24.67).

Median: 24.67

7. How do you determine the Mode for the given data?

Class Intervals: 0-10, 10-20, 20-30, 30-40

Frequency: 5, 8, 15, 12

Modal Class: 20-30

Solution:

1. (l = 20, h = 10, f_1 = 15, f_0 = 8, f_2 = 12).
2. Use formula: (text{Mode} = l + left(frac{f_1 – f_0}{2f_1 – f_0 – f_2}right) times h).
3. (text{Mode} = 20 + left(frac{15 – 8}{30 – 8 – 12}right) times 10 = 20 + 4.38 = 24.38).

Mode: 24.38