📊 statistics

1. **State the problem:** We have two paired samples representing measurements from the left and right leaves for 12 samples. We want to test if there is a significant difference b

1. **Problem Statement:** A doctor wants to test if a new medication reduces systolic blood pressure. We have paired data (before and after) for 10 patients. We will use a paired t

1. The problem is to find the sample size when the population size is 2000. 2. To calculate sample size, we often use formulas depending on the context, such as confidence level, m

1. The problem asks to identify the correct regression line equation from the given options. 2. A regression line equation is generally written as $$Y = mX + b$$ where $m$ is the s

1. **Stating the problem:** We have data points for screen time $X$ and corresponding sleep hours $Y$. We want to find a mathematical model that relates $Y$ to $X$. 2. **Choosing t

1. **State the problem:** We are given a list of daily expenses and asked to find the second quartile (Q2), which is the median of the data. 2. **Recall the formula and rules:**

1. **State the problem:** We want to determine who performed better relative to their event: the runner or the swimmer. 2. **Relevant formula:** To compare performances relative to

1. **Problem statement:** Find the values of $z_1$ and $z_2$ such that the area under the standard normal curve between $z_1$ and $z_2$ is $P(z_1 < Z < z_2) = 0.8558$. 2. **Underst

1. The problem asks for the probability that a standard normal variable $Z$ lies between $-2.59$ and $1.47$, i.e., $P(-2.59 < Z < 1.47)$. 2. For a standard normal distribution, pro

1. The problem asks for the area under the standard normal curve to the left of $z = -1.42$. 2. The standard normal distribution is a normal distribution with mean $\mu = 0$ and st

1. The problem asks to find the value of $k$ such that the area to the right of $k$ under the standard normal curve is $P(z > k) = 0.0096$. 2. This means we want to find the $z$-sc

1. The problem asks to find the value of $k$ such that the area to the right of $k$ under the standard normal curve is $P(z > k) = 0.0096$. 2. This means we want to find the $z$-sc

1. The problem asks for the area under the standard normal curve to the right of $z = -2.43$. 2. The standard normal distribution is symmetric about zero, and the total area under

1. **State the problem:** We have a sample data set: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. We want to find the new standard deviation if every observation is multiplied by 4.

1. **Problem Statement:** Calculate the harmonic mean $H$ using the formula $$H = \frac{\sum f}{\sum f \left(\frac{1}{x_i}\right)}$$ where $f$ is the frequency and $x_i$ is the mid

1. **State the problem:** We have a frequency distribution table for test marks with marks 4, 5, and 8, and frequencies 2, 4, and $n$ respectively. The mean mark is given as 6. We

1. The problem: Understand what standardisation means and how to apply it in problems. 2. Standardisation is a process used in statistics to transform data so it has a mean of 0 an

1. **Stating the problem:** We have a survey of 75 people with age and food preference data. We want to find how many people aged 25 or less like both spicy and sweet food.

1. The problem is about constructing histograms, either separately or together. 2. Histograms are graphical representations of data distribution, showing frequency of data interval

1. You asked to see a picture of histograms. 2. Histograms are graphical representations of data distribution, typically shown as bars.

1. **Problem Statement:** We have marks scored by 40 pupils in English and Mathematics tests grouped into intervals. We need to: (a) Draw two histograms on the same axes for Englis