📊 statistics

1. **Problem 1: Weekly Study Hours Variance and Standard Deviation** We have a frequency distribution of study hours for 100 students:

1. **State the problem:** We have a probability distribution for the number of games $X$ each child played: $X = \{2,3,4,5,6,7\}$ with probabilities $p(x) = \{0.05, 0.15, 0.15, 0.2

1. **Problem Statement:** We have a factorial experiment with three factors: Concentrated Feed (A) with 3 levels, Pasture (B) with 4 levels, and Farm (K) with 3 levels. We need to:

1. **Stating the problem:** We have yield data from three farms (A, B, C) with two factors: irrigation (whole plot factor) and fertilizer (sub-plot factor). We want to perform a sp

1. **State the problem:** We have a split-plot design experiment with two factors: grow media (whole-plot factor) and fertilizer formulation (sub-plot factor), replicated three tim

1. **Problem Statement:** We have a linear regression model for Trips: $$Trips = a + b \times Households + c \times Employment + \varepsilon$$

1. **Stating the problem:** We are given a histogram showing frequency density of office areas in intervals of 2 m², focusing on the intervals 16-18 m² and 18-20 m². 2. **Understan

1. **Problem Statement:** We want to understand the components and analysis steps in a Completely Randomized Design (CRD) model where $\mu$ is the overall true mean, $\tau_j$ is th

1. **Problem Statement:** You want to understand the basic principles of experimental design: Replication, Randomization, and Reduction of Error/Local Control, and their purposes.

1. **Problem Statement:** We are given times it took mice to navigate a maze, represented by dots on a line plot. We need to find the total time taken by the mice with the shortest

1. **State the problem:** We have rainfall amounts recorded at different locations with dots representing the number of locations receiving certain inches of rain. The dots are plo

1. **State the problem:** We are given the lengths of Avi's favorite songs as dots on a line plot at specific times: one dot at 4\frac{1}{4} minutes, one dot at 4\frac{3}{4} minute

1. **State the problem:** We want to determine if there is a significant difference in mean sodium amounts among three groups: Condiments, Cereals, and Desserts, using the between-

1. **Stating the problem:** We have data points representing hours spent studying ($x$) and money earned ($y$) for 10 students: (18, 23), (20, 21), (23, 20), (25, 19), (25, 21), (2

1. **Problem Statement:** We have a scatter plot showing the relationship between hours spent studying ($x$) and money earned ($y$) for 10 students. We need to (a) comment on the r

1. **State the problem:** We have data on absences and GPA for 10 students and want to forecast the GPA for a student with 7 absences. 2. **Calculate the linear regression line:**

1. **State the problem:** We have data on absences and GPA for 10 students. We want to forecast the GPA for a student with 5 absences and find the correlation coefficient $r$ betwe

1. **Stating the problem:** We have actual sales and two forecast methods (M1 and M2) for 6 days. We need to calculate:

1. **Stating the problem:** We have sales data for 7 weeks for each weekday. We want to find the seasonal index for Monday, Wednesday, and Friday, and then use the forecast for Wee

1. **Stating the problem:** We have a grouped frequency distribution table with class intervals and frequencies. We need to complete the table by calculating $d$, $fd$, $fd^2$, and

1. **Problem Statement:** We have data points representing hours spent studying ($x$) and money earned ($y$) by 10 students: (18, 23), (20, 21), (23, 20), (25, 19), (25, 21), (27,