📊 statistics

1. مسئله: در ۴۰ مرتبه پرتاب سکه، ۲۴ مرتبه شیر ظاهر شده است. می‌خواهیم فاصله اطمینان ۹۸٪ برای نسبت شیرها در تعداد نامحدود پرتاب سکه به دست آوریم. 2. فرمول: برای فاصله اطمینان نسبت $

1. **State the problem:** We want to test if the mean repair costs charged by the two branches, Taman U and Taman Daya, are different at a 5% significance level. 2. **Given data:**

1. **State the problem:** We want to find a 95% confidence interval for the population proportion $p$ of spare parts that are not usable. 2. **Given data:** Sample size $n=80$, sam

1. **Problem:** Given the data set 2, 1, 5, 4, find the variance. 2. **Formula for variance:**

1. **State the problem:** We have a sample of size $n=20$ from a normal distribution with sample standard deviation $s=5.8$ mg. We want to find a 90% confidence interval for the po

1. **State the problem:** We want to construct a 95% confidence interval for the mean length of computer chips produced, given a sample mean $\bar{x} = 1.15$ cm, sample standard de

1. The problem asks for the mean of the number 46 in a calculation. 2. The mean (or average) of a set of numbers is calculated by summing all the numbers and then dividing by the c

1. **Problem Statement:** Calculate the population mean and the sample mean separately given a data set. 2. **Formulas:**

1. **Problem:** Calculate the arithmetic mean (population mean, sample mean, median) of the Education Level data. 2. **Data:** Education Level values from the dataset: $[1,2,1,1,1,

1. **Stating the problem:** What is Statistics? 2. **Definition:** Statistics is a way to get information from data. It involves collecting, organizing, summarizing, analyzing, and

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

1. **Problem statement:** How to generate a random variable with a univariate log-concave density. 2. **Definition:** A univariate density $f(x)$ is log-concave if $\log f(x)$ is a

1. مسئله: محاسبه میانه (Median) برای داده‌های گروه‌بندی شده داده شده است. 2. فرمول میانه برای داده‌های گروه‌بندی شده:

1. **State the problem:** We want to test if there is a difference in taste ratings between fruit juice treated with Cold Plasma (CP) and without CP using matched pairs data from 1

1. The problem: Understanding when to use one-sample or two-sample t-tests. 2. One-sample t-test is used when you want to compare the mean of a single sample to a known population

1. Let's clarify the problem: You asked why the t statistic formula for two samples is not used in a certain context, even though there are two samples involved. 2. The t statistic

1. **State the problem:** We want to test if there is a difference in taste ratings between fruit juice treated with Cold Plasma (CP) and without CP using matched pairs data from 1

1. **State the problem:** Given data points $x = \{1,2,3,4,5,6\}$ and $y = \{5.6,4.6,4.5,3.7,3.2,2.7\}$, we need to find sums of squares and cross-products ($S_{xx}$, $S_{yy}$, $S_

1. The problem asks for the percentage of female clients who rated the tablet as not so easy to use, defined as a rating of 4 or lower. 2. From the bar graph data for females:

1. **Problem Statement:** Given data points $x = \{1,2,3,4,5,6\}$ and $y = \{5.6,4.6,4.5,3.7,3.2,2.7\}$, find the sums of squares and cross-products $S_{xx}$, $S_{yy}$, and $S_{xy}

1. **Problem Statement:** Given the data set of student marks: 2, 4, 4, 8, 4, 7, 1, 8, 3, 9, find the Mean, Median, Q1, Q3, Mode, Range, Mean Deviation, Quartile Deviation, Varianc