📊 statistics

1. **Problem Statement:** We have a grouped frequency distribution table with scores, frequencies, class marks, and related calculations. We want to understand the calculation of t

1. **State the problem:** Find the mean (average) of the numbers 2, 4, 6, 8, and 10. 2. **Formula for the mean:** The mean of a set of numbers is given by

1. The problem is to find the mode of the data set: 1, 1, 2, 3, 3, 3, 4. 2. The mode is the value that appears most frequently in a data set.

1. The problem is to find the formula for the mean of a set of numbers. 2. The mean, also called the average, is a measure of central tendency that summarizes a data set with a sin

1. **State the problem:** Find the mode of the data set 2, 3, 3, 5, 6. 2. **Definition:** The mode is the value that appears most frequently in a data set.

1. **Problem statement:** We are given a histogram showing the frequency density of paintings' ages in a gallery. We know 18 paintings are over 90 years old. We need to estimate ho

1. **State the problem:** We need to investigate different sampling methods and discuss how reliable conclusions drawn from data collected by these methods can be. 2. **Sampling me

1. **State the problem:** We want to estimate the number of paintings over 70 years old using the histogram data. 2. **Recall the formula for frequency:** Frequency = Frequency den

1. The problem asks to analyse and describe the distribution of data from each survey method compared to the population data. 2. We have four categories: Population data, Survey me

1. **State the problem:** We want to find the least-squares regression line to predict last year's budget ($y$) from the 2006 budget ($x$). 2. **Formula for least-squares regressio

1. **Problem Statement:** We have a frequency distribution of resistors with their resistances and counts. We need to find: (i) Modal resistance

1. The problem asks to estimate the standard deviation of calories in Child and Adult cereals based on the dotplots provided. 2. Standard deviation measures the spread of data arou

1. The problem asks which level of significance $\alpha$ to choose if the consequences of making a Type I error are severe. 2. A Type I error occurs when we reject a true null hypo

1. The problem asks to explain the difference between statistical significance and practical significance. 2. **Statistical significance** means that the sample statistic is unlike

1. The problem is to identify the correct null hypothesis ($H_0$) and alternative hypothesis ($H_1$) statements for a proportion $p$. 2. The null hypothesis ($H_0$) usually represe

1. The problem is to find the critical values for a Chi-Square distribution with significance level $\alpha = 0.01$ and sample size $n = 28$ for a two-tailed test. 2. The degrees o

1. **State the problem:** We have a sample of size $n=23$ from a normally distributed population with sample mean $\bar{x}=110$ and sample standard deviation $s=10$. We want to con

1. **Problem Statement:** We have three separate problems involving discrete random variables and their probability distributions.

1. The problem asks to identify the lower limit of the fifth class in a grouped frequency distribution of social interactions. 2. The classes are given as intervals: 20-24, 25-29,

1. **State the problem:** We are given a list of data values representing hours studied: 23, 24, 18, 20, 22, 15, 24, 25, 17, 25, 16, 18, 15, 20, 17, 21, 22, 24, 20, 18, 15, 16, 21,

1. **State the problem:** We are given a grouped frequency distribution of social interactions over a week and asked to find the lower limit of the eighth class. 2. **Understand th