📊 statistics

1. **Stating the problem:** Diberikan data dari dua stasiun pengukuran kadar ortofosfor:

1. **Problem Statement:** Suppose we have two independent samples from two different populations. The first sample has variance $s_1^2 = 16$ with sample size $n_1 = 25$, and the se

1. **State the problem:** We need to calculate the mean, median, lower quartile (Q1), and mode for the grouped data of weights of 120 articles. 2. **Given data:**

1. The problem states that the regression equation is $$Y=50+2X$$ where $Y$ is the sales revenue in thousands of dollars and $X$ is the number of sales calls made. 2. We need to fi

1. The problem asks for the mode of the data set: 6, 6, 7, 7, 8, 8, 8, 9. 2. The mode is the value that appears most frequently in a data set.

1. **State the problem:** We want to determine the relationship between the amount of fat consumed (x) and cholesterol level (y) based on the given data. 2. **Data given:**

1. Problem statement: Find the closest 3rd decile $D_3$ for the dataset: 50, 60, 55, 65, 70. 2. Formula and rules: The k-th decile $D_k$ corresponds to the $k\times10$th percentile

1. Masalani bayon qilish: Berilgan $f(x)$ uzluksiz tasodifiy miqdorning zichlik funksiyasi (PDF) sifatida berilgan. Bizga uning dastlabki to'rt markaziy momentlari va assimmetriya

1. **Problem Statement:** You are given quiz scores of 20 students: 70, 86, 74, 90, 80, 96, 84, 78, 70, 80, 86, 94, 68, 92, 80, 84, 80, 90, 74, 84.

1. **Problem Statement:** Given the covariance matrix $$\Sigma = \begin{pmatrix} 2 & 3 \\ 3 & 7 \end{pmatrix}$$, compute the eigenvalues and the proportion of total variance explai

1. **Problem Statement:** Find the probabilities for a standard normal variable $Z$ for the following cases: (i) $P(Z > 1.09)$

1. The problem asks to find the probability that a standard normal random variable $Z$ is less than 2.4, i.e., $P(Z < 2.4)$. 2. We use the standard normal distribution table or a c

1. The problem asks to find the probability $P(Z > -0.58)$ where $Z$ is a standard normal variable. 2. The standard normal distribution is symmetric about zero, and probabilities a

1. **Problem:** Given 30% of bank customers are female, find probabilities for 10 randomly selected customers. 2. **Formula:** Use binomial probability formula $$P(X=k) = \binom{n}

1. **State the problem:** We want to test if there is enough evidence to reject the claim that the average home price in Beaver County is $60,000 at significance level $\alpha = 0.

1. **State the problem:** We want to test if there is enough evidence to reject the claim that the average price of a home sold in Beaver County is $60,000 at a significance level

1. The problem is to understand how to organize and display data using tables in statistics. 2. A table in statistics is a way to arrange data in rows and columns to make it easier

1. **Problem Statement:** Calculate the coefficient of skewness and kurtosis for the exam scores \{60, 62, 65, 68, 70, 70, 72, 74, 75, 75, 76, 78, 80, 82, 85, 88, 90, 92, 95, 98\}

1. The problem is to understand the concepts of mean, median, and mode (modus) in statistics. 2. **Mean** is the average of a set of numbers. It is calculated by summing all the nu

1. **Problem statement:** Calculate the coefficient of skewness and kurtosis for the exam scores \{60,62,65,68,70,70,72,74,75,75,76,78,80,82,85,88,90,92,95,98\} and interpret the d

1. **State the problem:** Find the interquartile range (IQR) of the data set: 8, 4, 7, 6, 15, 12, 16, 18. 2. **Sort the data:** Arrange the numbers in ascending order: 4, 6, 7, 8,