📊 statistics

1. **Problem 1 (Two marks):** Calculate the mean of the data set: 5, 8, 12, 20, 25. 2. **Solution:**

1. **Problem Statement:** Find the median and standard deviation of the given data set. 2. **Median:** The median is the middle value when the data is ordered from least to greates

1. **Problem Statement:** Given a grouped frequency distribution of employee performance rates, we need to find:

1. **Problem Statement:** Test the surveyor’s claim using a chi-square goodness-of-fit test with significance level $\alpha = 0.01$. 2. **Chi-square goodness-of-fit test formula:**

1. **State the problem:** We are given the number of accidents in a city during a week and want to test if the accidents are uniformly distributed over the days of the week. 2. **D

1. The problem states that $H_0: \mu_1 = \mu_2$, which is a hypothesis test where the null hypothesis claims the means of two populations are equal. 2. This is a common setup in st

1. **Problem Statement:** We want to find the 70th percentile $y^*$ of the fish length distribution, meaning 70% of fish lengths are less than $y^*$ and 30% are greater. 2. **Formu

1. Problem: Carla rolls a fair six-sided die. She wins 12 if she rolls a 6, but loses 3 for any other number. Find the expected value. Formula: Expected value $E(X) = \sum [x \cdot

1. **Problem:** Test if there is a difference in the age of onset of Alzheimer's symptoms between men and women at a 5% significance level. 2. **Hypotheses:**

1. **Problem a:** Find the midpoint of the first group 0 - 9. The midpoint of a group is the average of the lower and upper boundaries.

1. **Problem:** Test if there is a difference in the age of onset of Alzheimer’s symptoms between men and women. 2. **Hypotheses:**

1. **State the problem:** Find the mean (average) of the numbers 1, 2, 2, 5, 6, 7, 8. 2. **Formula for the mean:** The mean of a set of numbers is given by

1. **بيان المسألة:** لدينا قيم البيانات التالية: 20، 30، 50، 60، 70، 80.

1. The problem is about finding the median of a set of numbers arranged in ascending order. 2. The median is the middle value when the numbers are sorted.

1. The problem is to find the number that has the highest chance of appearing from the given list: (75, 89, 89, 62, 62, 40, 40, 67, 67, 43, 43, 80, 80). 2. To solve this, we need t

1. **State the problem:** We want to determine if there is a significant difference between the performance of males and females in Math based on the given paired data. 2. **Hypoth

1. **State the problem:** Determine whether there is a significant difference between the performance of males and females in Math using hypothesis testing. 2. **State the hypothes

1. **Problem:** Determine if there is a significant difference between the performance of males and females in Math using hypothesis testing. 2. **Step 1: State the hypotheses.**

1. **Problem Statement:** Determine whether the new treatment is comparatively superior to the conventional treatment based on the given data: | Treatment | Favourable | Non Fav

1. **Stating the problem:** We want to understand the concepts of variance and coefficient of variance, which are important statistical measures. 2. **Variance:** Variance measures

1. The problem is to find the average (mean) of the given numbers: 85, 79, 82, 78, 65, 43, 66, 69, 80, 91, 40, 79, 81, 70, 55, 60, 71, 50, 77, 75, 74, 74, 80. 2. The formula for th