📊 statistics

1. **State the problem:** We want to find the probability of exactly $x=1$ successes in $n=100$ trials with success probability $p=0.1$ using the binomial distribution. 2. **Formul

1. Stating the problem: We need to find the average of all the individual category averages given in the images, then find the average of those averages. 2. Extract all category av

1. The problem is to find the mean $\bar{x}$ from the given frequency distribution table. 2. The formula for the mean of grouped data is:

1. **Problem Statement:** We want to understand Principal Component Analysis (PCA) in high dimensions, focusing on dimension reduction, spectral properties of covariance matrices,

1. **State the problem:** We need to find the quadratic regression equation of the form $$y = ax^2 + bx + c$$ that best fits the given data points. 2. **Given data:**

1. **State the problem:** We are given the runs scored by cricket team A: 2, 3, 4, 6, 21, 26, 27, 32, 34, 61, 72. The interquartile range (IQR) of runs scored by cricket team B is

1. The problem is to simplify and evaluate the expression: $$\sqrt{\frac{(1.16-1.154)^2+(1.14-1.154)^2+(1.15-1.154)^2+(1.16-1.154)^2+(1.15-1.154)^2+(1.15-1.154)^2+(1.16-1.154)^2+(1

1. **State the problem:** We want to find the Spearman's Rank correlation coefficient between tourists' and locals' scores for 7 Penang attractions to see if their opinions are sim

1. **Problem Statement:** Calculate the linear regression equation of maintenance cost $y$ on building age $x$ using the least squares method, estimate the maintenance cost for a b

1. **State the problem:** We are given an ANOVA table with partial data and need to complete the table and calculate the F-statistic to test if diet affects weight gain in rats.

1. The problem states that a total of 15 goals were scored by three players: Keshore, Lester, and Richard. 2. The symbols represent goals: ◎ is a full goal, and ◐ is a half goal.

1. The problem states that a total of 15 goals were scored by three players: Kanhou, Loser, and Richard. 2. The table shows the number of goals each player scored represented by ci

1. **Problem Statement:** We have household income data following a Normal Distribution with mean $\mu=3000$ and standard deviation $\sigma=500$.

1. The problem involves calculating the Z-score, which measures how many standard deviations a data point $x$ is from the mean $\mu$. 2. The formula for the Z-score is:

1. **Problem Statement:** We have wait times at a coffee shop that follow a normal distribution with mean $\mu=8$ minutes and standard deviation $\sigma=2$ minutes. We want to expl

1. **Problem Statement:** We have a contingency table showing proportions of loan types (Fixed Rate (FR) and Adjustable Rate (ADJ)) and loan purposes (Home (H), Automobile (A), Per

1. The problem asks for the average (mean) number of toys in 6 boxes with counts: 4, 10, 7, 0, 4, 5. 2. The formula for the average (mean) is:

1. **State the problem:** We need to find the median of the data set: 0, 4, 1, 5, 2, 1, 6, 4, 6, 3, 0, 6, 3, 0, 2, 5. 2. **Recall the median definition:** The median is the middle

1. **State the problem:** We want to find the fraction of Juan's shifts where total sales were $225$ or more based on the given box plot. 2. **Understand the box plot:** The box pl

1. The problem is to find the median of the data set: 11, 4, 6, 15, 21, 19, 0, 19, 25. 2. The median is the middle value when the data is arranged in ascending order.

1. The problem involves analyzing two box plots representing points scored. 2. The first box plot has a box from about 5 to 20, median near 17, whiskers from 0 to 25.