📊 statistics

1. The problem involves analyzing the given data set: 30, 20, 40, 20, 30, 60, 80, 20, 40, 20. 2. First, let's state the problem clearly: We need to find measures of central tendenc

1. The user has provided a list of data points: 30, 20, 40, 20, 30, 60, 80, 20, 40, 20. 2. Since the user mentioned (i), (ii), (iii), etc., but did not specify explicit questions,

1. The problem involves computing sums and averages from the given data set: 30, 20, 40, 20, 30, 60, 80, 20, 40, 20. 2. To find the sum, use the formula:

1. The problem involves calculating the weighted average and percentage score for each feedback parameter based on the given ratings. 2. The formula for weighted average is:

1. The problem is to calculate the weighted average and percentage score for each feedback parameter, then find the overall average and overall percentage. 2. The formula for weigh

1. The problem states that sugar bags have a mean weight of 1.06 kg and 2.5% are underweight (less than 1 kg). We want to find the standard deviation $\sigma$ in grams. 2. We model

1. **Fish length for restaurants:** The fish lengths are normally distributed with mean $\mu=48$ cm and standard deviation $\sigma=5$ cm.

1. The problem is to understand when to reject the null hypothesis ($H_0$) in hypothesis testing for p-tests, t-tests, and chi-squared tests. 2. The general rule is: reject $H_0$ i

1. Let's start by stating the problem: You want to understand when to reject the null hypothesis ($H_0$) in a t-test and a chi-squared test, and whether the rejection criteria foll

1. The problem is about understanding the choice of significance level in hypothesis testing. 2. The significance level, often denoted as $\alpha$, is the threshold probability for

1. **State the problem:** You want to determine if the BMI scores at your college are significantly different from the general population, given your null hypothesis $H_0$: The BMI

1. Let's clarify the problem: You are asking if when calculating a z-value (often in statistics), you should use only sample data to get the most accurate answer. 2. The z-value fo

1. **Problem statement:** Calculate the probability that the mean BMI of a random sample of 50 healthy 19 to 24-year-olds is greater than or equal to 27.1 kg/m2, given the populati

1. Let's clarify the problem: You are asking about the third quartile (Q3) of a data set and whether the value 15 is correct. 2. The third quartile (Q3) is the value below which 75

1. لنبدأ بفهم السؤال: لماذا يجب أن يكون المتوسط من مضاعفات 10؟ 2. المتوسط هو مجموع القيم مقسومًا على عددها، وعادةً ما نستخدم مضاعفات 10 لتسهيل الحسابات وجعل النتائج أكثر وضوحًا وقا

1. **State the problem:** Calculate the standard deviation of a data set with $n=5$, $\sum x=20$, and $\sum x^2=225$. 2. **Recall the formula for standard deviation (sample):**

1. **State the problem:** We need to find the lower and upper fences of the data set using the formulas: $$\text{Lower fence} = \mu - k\sigma$$

1. **State the problem:** We need to find the standard deviation $\sigma$ of the data set: 1, 1, 2, 7, 8, 9, 10, 10, 11, 12, 20. 2. **Recall the formula for standard deviation:**

1. **State the problem:** We have data for years of service $x$ and paid days off $y$. We want to find the line of best fit using the least squares method and then estimate paid da

1. **Problem Statement:** We have a physics class with 800 students whose test scores are normally distributed with mean $\mu=75$ and standard deviation $\sigma=7$. We need to find

1. Problem: A man tosses a fair coin 196 times. Find the probability that he obtains between 105 and 112 heads. Step 1: Define the problem using the binomial distribution with para