📊 statistics

1. **State the problem:** Given a set of values $x$ with mean $\bar{x} = 9$, and the corresponding deviations $(x - \bar{x})$ and squared deviations $(x - \bar{x})^2$, verify the c

1. **Problem Statement:** We have two predictors $X_1$ and $X_2$ and a response variable $Y$ with observations: $X_1 = [1,2,4,7,10,12,14]$

1. The problem asks to calculate the mean and standard deviation of the number of comments for 10 opinion articles: {15, 25, 10, 30, 20, 18, 22, 12, 28, 17}. 2. First, calculate th

1. **State the problem:** We need to estimate the population variance and standard deviation with 98% confidence for two different populations based on samples of size 10.

1. **State the problem:** Calculate the range and standard deviation for daily website traffic data for the Politics and Sports sections, then compare variability. 2. **Identify th

1. **Problem statement:** A family recorded their monthly electricity bills over 6 months: 1200, 1250, 1300, 1280, 5000, 1270. We are asked to find (a) the mean and median of the b

1. The problem is to determine who performed better based on z-scores. 2. To find who performed better, recall that a higher z-score means better performance relative to the mean.

1. Problem: Compare performances using z-scores. 1.a) Ping's z-score = 1.60, Pong's z-score = 1.75.

1. **State the problem:** We have ratings for a mobile phone from 1 to 5 stars and the number of users who gave each rating. We need to find: a) The weighted average rating.

1. **Problem statement:** We have commute times over 7 days: 30, 28, 35, 40, 32, 100, 31 minutes. 2. **Calculate the mean commute time:**

1. **Stating the problem:** We have marks and their corresponding weights for five subjects. We want to calculate the weighted mean of the marks and compare it to the simple mean.

1. **Problem Statement:** We have monthly incomes (in thousands of BDT) of 9 employees: 22, 25, 27, 24, 30, 21, 100, 23, 26. We need to find the mean and median income and determin

1. **Problem statement:** We want to find the areas under the standard normal distribution curve for the following cases: (a) Between $z=0$ and $z=1.77$

1. **Stating the problem:** We have typing speeds (words per minute) from four word processors (A, B, C, D), with multiple measurements each. We want to test if the observed differ

1. **State the problem:** We want to find the Pearson product-moment correlation coefficient $r$ between the years of higher education (variable $X$) and monthly salary in thousand

1. **Problem (d): Compute the 95% confidence interval for $\beta_1$** To compute the confidence interval for $\beta_1$, we use the formula:

1. **State the problem:** We have typing speed data from four word processors A, B, C, D. We want to test if the differences in their mean typing speeds are statistically significa

1. **State the problem:** We want to test if there is a significant difference among the means of typing speeds (words per minute) of four different word processors (A, B, C, D). 2

1. The problem asks for t-tests for four groups labeled a, b, c, and d. 2. A t-test compares means of two groups to see if they are significantly different.

1. **Stating the problem:** We have four word processors (A, B, C, and D) with observations of words typed per minute. We want to test if the differences among the means of these f

1. **Problem 1: 90% Confidence Interval for Mean Annual Income** Given: