📊 statistics

1. **Problem Statement:** A researcher selected every 20th name from a list of 500 Grade 10 students. 2. **Identify the sampling method:** This is systematic sampling where every $

1. **State the problem:** The Read and Feed restaurant surveyed 150 customers who chose to answer an online survey printed on receipts. 60% of these respondents said they were sati

1. **Problem:** Find the regression lines of y on x and x on y for the data points given. 2. **Formula:** The regression line of y on x is given by $$y = mx + c$$ where $$m = \frac

1. **State the problem:** We need to compute the mean (average) of the given day sales: 1203.00, 1203.21, 2013.99, 2103.12, and 1231.00. 2. **Formula for the mean:** The mean of $n

1. **State the problem:** We have a grouped frequency table of daily visitors to a gym with class intervals of width 10. We need to calculate the mean number of daily visitors. 2.

1. **Problem statement:** Given detection times: 12, 14, 13, 15, 13, 16, 14, 13, 17, 12, we need to compute various statistics. 2. **Sum of all detection times:**

1. **State the problem:** We need to find the correlation coefficient $r$ for the data pairs $(x, y)$ where $x$ is the number of breakfasts eaten and $y$ is the GPA. 2. **Recall th

1. **Problem Statement:** We are given a list of times (in minutes) taken by people to solve a puzzle: 8, 7, 20, 24, 10, 15, 14, 10, 8, 16, 12, 24, 29. 2. **What is a Stem-and-Leaf

1. **State the problem:** We are given a list of times in minutes: 8, 7, 20, 24, 10, 15, 14, 10, 8, 16, 12, 24, 29. 2. **What is a stem-and-leaf diagram?** It is a way to organize

1. **State the problem:** We have a survey of 300 students about their movie-going frequency and genre preference. We want to find: (a) The percentage of students who go to the mov

1. The problem asks for the mode of the data, which is the category with the highest percentage of customers. 2. From the data given:

1. **Stating the problem:** We have a random variable $X$ representing the number of customers who order takeout in a day at a café. The values of $X$ are $0, 1, 2, 3,$ and $4$ or

1. **State the problem:** We want to test if the mean length of novels written by the club members is greater than 50,000 words at a significance level $\alpha = 0.10$. 2. **Set hy

1. **نص المشكلة:** لدينا توزيع تكراري للأجور الأسبوعية لعدد 30 عاملاً موزعة على فئات الأجور مع تكراراتها. 2. **البيانات:**

1. **Problem:** A new student with a test score of 8 joins a group whose mean score is 344 and median score is 335. We need to find the new mean and median positions (lines A, B, C

1. **State the problem:** We have a population of 8 cards numbered 1 to 8. We draw samples of size 3 without replacement and want to find the sampling distribution of the sample me

1. The Wishart distribution is a probability distribution that generalizes the chi-squared distribution to multiple dimensions. 2. It is used to describe the distribution of sample

1. **State the problem:** We have 30 people: 20 men and 10 women. Men's mean weight $\mu_m = 65$ kg, variance $\sigma_m^2 = 56.25$ kg$^2$.

1. The problem asks for the mean (average) of the temperatures given: -9, -5, 0, 1, and -2 degrees Celsius. 2. The formula for the mean of a set of numbers is:

1. **State the problem:** We need to find the mean number of emails sent on days beginning with the letter S or T. 2. **Identify the days:** Days starting with S are Saturday and S

1. **State the problem:** We want to understand how weather variables (temperature $X_1$, humidity $X_2$, rainfall $X_3$) affect household electricity consumption $Y$ using a regre