📊 statistics

1. مسئله: ضریب تغییرات داده‌های ۶، ۲، ۱، ۲، ۱۲ را بیابید. 2. فرمول ضریب تغییرات (Coefficient of Variation) به صورت زیر است:

1. The problem is to understand and use the formula for covariance. 2. Covariance measures how two random variables change together. The formula for covariance between two variable

1. **Problem Statement:** We have a population divided by age groups and poverty status. We want to find:

1. **State the problem:** We need to find the mean (average) number of trips to the mall last month based on the given frequency data. 2. **Understand the data:** The number of tri

1. **State the problem:** We need to find the mean (average) number of doctor visits last year based on the given frequency data. 2. **Recall the formula for the mean:**

1. **State the problem:** We want to find the mean number of pictures painted based on the given frequency data. 2. **Data interpretation:** The horizontal axis shows the number of

1. Problem: Janice recorded scores shown on the line plot and we must find the mean of the numbers. 2. Data: There is 1 observation at 1, 2 at 2, 4 at 3, 3 at 4, and 1 at 5.

1. **State the problem:** We are given the number of winter hats owned by readers and their frequencies. We need to find the mean number of winter hats. 2. **List the data:**

1. **State the problem:** Find the median of the numbers 3.8, 7.5, 9.4, 5.3, 3.8, 8.9. 2. **Recall the formula and rules:** The median is the middle value of a data set when the nu

1. **Problem Statement:** We want to fit a multiple linear regression model to forecast Quantity Demand ($Q$) based on Price ($P$) and Income ($I$).

1. **Problem Statement:** Find the mean, median, and mode of the grouped data given by the class intervals and frequencies. 2. **Given Data:**

1. **State the problem:** We want to find the P-value for testing the hypothesis \(H_0: \mu = 6\) against \(H_A: \mu < 6\) given a sample mean critical region \(\overline{X} < 5.8\

1. **Problem Statement:** We have a sample of complaints per day over 10 days: 3, 5, 2, 4, 6, 3, 4, 7, 5, 4. We want to find the Maximum Likelihood Estimate (MLE) of the Poisson pa

1. **Problem Statement:** We want to find the critical value $c$ such that the null hypothesis $H_0: \mu = 20$ is rejected if the sample mean $\overline{X} > c$ at a 5% level of si

1. **Problem Statement:** Given $X_1, X_2, \ldots, X_n$ are i.i.d. Uniform$(0, \theta)$ random variables, and an estimator $\hat{\theta} = \frac{k}{n} \sum_{i=1}^n X_i$, determine

1. **State the problem:** We have a probability distribution with values of $x$ and their probabilities $P(X)$. We need to complete the table, find the mean ($\mu$), variance ($\si

1. **Problem statement:** Tim wants to sample 160 fish from a lake containing 450 mirror carp, 300 leather carp, and 850 common carp to investigate their health.

1. The problem is to represent the number of apples sold over 4 days using a bar graph. 2. A bar graph visually displays data with rectangular bars where the length of each bar is

1. **Problem statement:** Calculate a 96% confidence interval for the population mean height of a species of deer given a sample mean of 1.42 m, sample size 150, and population sta

1. **Problem statement:** We have 80 items on sale with discounts up to 60. We want to find the upper and lower quartiles and the interquartile range (IQR) of the discounts from th

1. **Problem Statement:** Calculate the average and standard deviation of the number of accidents for the years 2078 and 2079. 2. **Data:**