It looks like the image you uploaded contains an exercise with multiple mathematical tasks related to data classification, summation, and evaluation. Specifically, the exercise includes:

1. Collecting data from your household categorized using nominal, ordinal, interval, and ratio scales.
2. Explaining scenarios involving sampling methods.
3. Evaluating some mathematical expressions for given values.

The specific part I can help you with from the image includes evaluating the provided summation expressions.

Let's break down the tasks and evaluate them one by one.

Part a:

You're given:

• $x_1 = 5, x_2 = 7, x_3 = -4, x_4 = 2, x_5 = 5$

You need to evaluate:

1. $\sum_{i=1}^{5} x_i$
2. $\sum_{i=1}^{5} x_i^2$
3. $\sum_{i=1}^{5} (x_i - 3)$

Part b:

You're given:

• $x_1 = -4, x_2 = 5, x_3 = 2, x_4 = 2$
• $y_1 = 2, y_2 = 1, y_3 = -2, y_4 = -3$

You need to evaluate:

1. $\sum_{i=1}^{4} (x_i + y_i)$
2. $\sum_{i=1}^{4} x_i$
3. $\sum_{i=1}^{4} y_i$

Let's go step-by-step for each one!

I’ll first handle part a and perform the necessary calculations. Given values for part a x_values_a = [5, 7, -4, 2, 5]

1. Sum of x_i

sum_x_a = sum(x_values_a)

2. Sum of x_i^2

sum_x_squared_a = sum(x**2 for x in x_values_a)

3. Sum of (x_i - 3)

sum_x_minus_3_a = sum(x - 3 for x in x_values_a)

sum_x_a, sum_x_squared_a, sum_x_minus_3_aFor Part a, the evaluations are as follows:

1. $\sum_{i=1}^{5} x_i = 5 + 7 + (-4) + 2 + 5 = 15$
2. $\sum_{i=1}^{5} x_i^2 = 5^2 + 7^2 + (-4)^2 + 2^2 + 5^2 = 25 + 49 + 16 + 4 + 25 = 119$
3. $\sum_{i=1}^{5} (x_i - 3) = (5 - 3) + (7 - 3) + (-4 - 3) + (2 - 3) + (5 - 3) = 2 + 4 + (-7) + (-1) + 2 = 0$

Now, I’ll proceed to Part b and evaluate the corresponding expressions. Given values for part b x_values_b = [-4, 5, 2, 2] y_values_b = [2, 1, -2, -3]

1. Sum of (x_i + y_i)

sum_x_plus_y_b = sum(x + y for x, y in zip(x_values_b, y_values_b))

2. Sum of x_i

sum_x_b = sum(x_values_b)

3. Sum of y_i

sum_y_b = sum(y_values_b)

sum_x_plus_y_b, sum_x_b, sum_y_bFor Part b, the evaluations are as follows:

1. $\sum_{i=1}^{4} (x_i + y_i) = (-4 + 2) + (5 + 1) + (2 + (-2)) + (2 + (-3)) = -2 + 6 + 0 + (-1) = 3$
2. $\sum_{i=1}^{4} x_i = -4 + 5 + 2 + 2 = 5$
3. $\sum_{i=1}^{4} y_i = 2 + 1 + (-2) + (-3) = -2$

If you need further details or have any questions about the calculations, feel free to ask!

Here are some related questions you might find useful:

1. What is the difference between nominal, ordinal, interval, and ratio data?
2. How do you calculate the sum of squares for a data set?
3. What is the importance of sampling methods in data collection?
4. How do you handle outliers in data when performing summations?
5. What are some practical examples of data that can be classified as ordinal?

Tip: To avoid mistakes when working with summations, it's helpful to organize your data in a table or list format, which helps in ensuring each term is correctly included.