Let's address the two tasks presented in the image:

Question 1: Correlation Coefficient

We are tasked to calculate the correlation coefficient for the given data:

Steps:

1. Calculate the Mean of X and Y:

   • Mean of $X$ ($\bar{X}$): $\frac{\text{Sum of X}}{\text{Number of values}}$
   • Mean of $Y$ ($\bar{Y}$): $\frac{\text{Sum of Y}}{\text{Number of values}}$

2. Calculate Deviations:

   • $(X - \bar{X})$ and $(Y - \bar{Y})$

3. Calculate the Products of Deviations:

   • $(X - \bar{X})(Y - \bar{Y})$

4. Calculate Squared Deviations:

   • $(X - \bar{X})^2$ and $(Y - \bar{Y})^2$

5. Plug into the Correlation Formula:

   • $r = \frac{\sum (X - \bar{X})(Y - \bar{Y})}{\sqrt{\sum (X - \bar{X})^2 \cdot \sum (Y - \bar{Y})^2}}$

Let me calculate this for you.

Question 2: Frequency Distribution Table

The provided data is: $0.5, 1.0, 1.5, 1.0, 2.0, 2.5, 2.0, 3.0, 2.5, 3.5, 4.0, 4.5, 3.0, 2.5, 2.0, 1.0, 0.5, 2.5, 3.0, 3.5, 4.5, 5.0, 5.5, 5.0, 4.0, 3.0, 3.5, 2.0, 1.5, 2.0, 2.5, 3.5, 4.0, 4.5, 5.5, 5.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.5, 0.5, 1.5, 2.5, 3.5, 4.5$

We need to divide the data into 6 classes, starting with the first class as $0.0 - 0.9$.

Steps:

1. Define the Class Intervals:

   • $0.0-0.9, 1.0-1.9, 2.0-2.9, 3.0-3.9, 4.0-4.9, 5.0-5.9$

2. Tally the Frequencies:

   • Count how many values fall into each interval.

3. Create the Frequency Distribution Table.

Let me process these for you.import pandas as pd import numpy as np

Data for Question 1 (Correlation Coefficient)

ages = np.array([2, 4, 5, 6, 8, 11]) # X values resale_values = np.array([18, 15, 11, 8, 7, 5]) # Y values

Step 1: Calculate means

mean_x = np.mean(ages) mean_y = np.mean(resale_values)

Step 2: Calculate deviations

deviation_x = ages - mean_x deviation_y = resale_values - mean_y

Step 3: Calculate product of deviations

product_deviation = deviation_x * deviation_y

Step 4: Calculate squared deviations

squared_deviation_x = deviation_x ** 2 squared_deviation_y = deviation_y ** 2

Step 5: Correlation coefficient formula

numerator = np.sum(product_deviation) denominator = np.sqrt(np.sum(squared_deviation_x) * np.sum(squared_deviation_y)) correlation_coefficient = numerator / denominator

Data for Question 2 (Frequency Distribution)

data = [ 0.5, 1.0, 1.5, 1.0, 2.0, 2.5, 2.0, 3.0, 2.5, 3.5, 4.0, 4.5, 3.0, 2.5, 2.0, 1.0, 0.5, 2.5, 3.0, 3.5, 4.5, 5.0, 5.5, 5.0, 4.0, 3.0,