📊 statistics

1. **Problem Statement:** Calculate the arithmetic mean, harmonic mean, geometric mean, and quadratic mean of the ages 10, 15, and 20. 2. **Formulas:**

1. The problem is to understand what the standard deviation is. 2. Standard deviation is a measure of how spread out numbers are in a data set.

1. The problem asks: Why do we need standard deviation if we already have variance? 2. Variance measures the average squared deviation from the mean, given by the formula:

1. **Problem Statement:** Find the area under the standard normal curve to the left of the given Z-values: a. $Z = -2.48$, b. $Z = 3.00$, c. $Z = 2.42$, d. $Z = 0.99$. 2. **Formula

1. The problem is to understand what variance means in statistics. 2. Variance measures how spread out a set of numbers is around the mean (average).

1. The problem is to understand why population variance and sample variance have different formulas. 2. Population variance measures the spread of an entire population and is calcu

1. The problem is to find the mean (average) of the given list of numbers. 2. The formula for the mean of a set of numbers $x_1, x_2, \ldots, x_n$ is:

1. **Problem Statement:** Find the mean electricity consumption and identify the modal class from the given frequency distribution. 2. **Given Data:**

1. **Problem Statement:** You flip four coins. Let $X$ be the number of heads obtained. 2. **Sample Space:** Each coin can be Head (H) or Tail (T). The sample space for four coins

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