📊 statistics

1. **State the problem:** Find the median of the given grouped data representing marks and number of students. 2. **Given data:**

1. **Stating the problem:** We have data for consumption (Y), income (X), and a dummy variable for gender (D). We want to find the regression coefficients $b_1$ (for income), $b_2$

1. **State the problem:** Find the range, mean, median, and mode of the fractions: $3 \frac{1}{3}$, $4 \frac{1}{2}$, $5 \frac{1}{6}$, $3 \frac{2}{3}$, $4 \frac{5}{6}$, $3 \frac{1}{

1. **State the problem:** We have a random variable $X$ representing the number of three-point shots made by a basketball player with the distribution: $$\begin{array}{c|cccc}

1. The problem asks us to compare the number of residents who chose Mouse and Bird as their favorite pet from a poll of 145,000 residents. 2. We are given the percentages for each

1. **Stating the problem:** We have a circle graph (pie chart) showing revenue distribution among six publication types: Textbooks, Cookbooks, Magazines, Paperbacks, Poetry, and No

1. **State the problem:** We have data points of specific gravity $x$ and percentage yield $y$ of petroleum gas. We want to estimate $y$ when $x=50$. 2. **Method:** Use linear inte

1. **Problem statement:** Find the coefficients $a$ and $b$ in the linear regression equation $y = bx + a$ for the given data points where $x$ is the % level of engagement and $y$

1. **Problem Statement:** We want to compute probabilities and percentiles using the standard normal distribution, which is a normal distribution with mean $\mu=0$ and standard dev

1. **State the problem:** We want to find how many students out of 1,500 spent more than 8 hours on social media, assuming the time spent follows a standard normal distribution. 2.

1. **Problem statement:** We have 500 candidates with marks normally distributed with mean $\mu=40$ and standard deviation $\sigma=10$.

1. **Problem statement:** We want to estimate the probability that a lion lives less than 7.2 years given that lion lifespans are normally distributed with mean $\mu = 10$ years an

1. **Problem statement:** We have exam scores normally distributed with mean $\mu=70$ and standard deviation $\sigma=5$. We want to find the proportion of scores between 68 and 73.

1. **Problem:** Find the percentage of students with weights between 123.2 kg and 138.4 kg, given weights are normally distributed with mean $\mu=134.6$ kg and standard deviation $

1. The value 0.9979 is typically found in statistical tables, such as the standard normal distribution (Z) table. 2. It represents the cumulative probability up to a certain Z-scor

1. **Problem statement:** We are given a normally distributed height of students with mean $\mu=125$ cm and standard deviation $\sigma=3.5$ cm. We want to find the percentage of st

1. **Stating the problem:** We have monthly rainfalls modeled as independent and identically distributed normal random variables with mean $\mu = 20$ cm and variance $\sigma^2 = 12

1. **Stating the problem:** We have monthly rainfalls that are independent and identically distributed normal random variables with mean $\mu = 20$ cm and variance $\sigma^2 = 12$

1. The problem asks us to estimate the number of children for whom $50 < m \leq 80$ minutes based on the histogram data. 2. The histogram shows frequency density for intervals of t

1. The problem is to find the mean value, which is given as 191.13. 2. The mean (average) of a set of numbers is calculated using the formula:

1. **Problem statement:** We have harvest data (kg) from 30 farms: 335, 171, 126, 71, 70, 312, 143, 50, 226, 106, 233, 123, 244, 138, 331, 221, 200, 325, 342, 83, 53, 206, 305, 104