📊 statistics

1. The problem asks us to calculate the mean (average) volume of gas released from the given data. 2. The volumes given are: $32, 35, 28, 30, 30$ cm$^3$.

1. **State the problem:** Calculate the mean (average) of the values 8, 9, 7, 2, and 4. 2. **List the values:** The numbers are 8, 9, 7, 2, and 4.

1. **Problem:** For test $H_0: \mu=100$ vs $H_1: \mu>100$, sample $z=2.15$. Find the p-value. 2. This is a right-tailed test so p-value = $P(Z \geq 2.15)$.

1. The problem asks for the most effective graph type to display proportions of different types of waste in a landfill. 2. A pie chart is ideal for showing proportions or percentag

1. **State the problem:** We are given a pie chart representing 120 gym members' daily exercise amounts. The chart sections are: - 162° for "< 30 minutes"

1. Find the mode for frequency distribution: Given marks intervals and frequencies: 0-10(7), 10-20(14), 20-30(13), 30-40(12), 40-50(20), 50-60(11), 60-70(15), 70-80(8).

1. Problem 27: Given mode = 55, find $x$ in frequency distribution: | Class | 0-15 | 15-30 | 30-45 | 45-60 | 60-75 | 75-90 |

1. Stating the problem: We need to find what percentage of Graduates joined the HR team last year. 2. Collect the data:

1. The problem asks for the difference between the highest and lowest marketing campaign reach percentages for Poland. 2. The reported percentages for Poland are 80%, 65%, 49%, and

1. **State the problem:** We need to identify which mistake Katie made in her stem-and-leaf diagram for the caterpillar lengths.

1. The problem requires us to organize the given weights (kg) into an ordered stem-and-leaf diagram. 2. First, list all weights in order from smallest to largest:

1. We are given a set of weights in kilograms: $0.3, 0.4, 0.9, 0.1, 0.2, 1.0, 0.2, 1.1, 0.4, 1.3, 1.6, 1.1, 2.3, 0.2$. 2. Our goal is to create an ordered stem-and-leaf diagram. Th

1. The problem is to fill in the missing row for the stem-and-leaf diagram showing the number of visitors to a cafe each day. 2. We are given visitor numbers: 102, 115, 91, 113, 94

1. **Stating the problem:** We are given a frequency polygon representing heights of members in a netball club. Our task is to estimate the mean height to 1 decimal place. 2. **Ide

1. The problem asks for the median of the numbers: 12, -6, -9, 1, -13. 2. To find the median, first arrange the numbers in ascending order.

1. مسأله: بررسی تفاوت معنی دار در میانگین نمرات سه گروه درمانی A، B، و C با استفاده از تحلیل واریانس (ANOVA) در سطح معنی داری ۵٪. 2. داده‌ها:

1. مسئله: بررسی اینکه آیا تفاوت معنادار آماری بین سه روش درمانی A, B, و C در کاهش میزان افسردگی وجود دارد یا خیر بر اساس نمرات داده شده با سطح معنی داری 0.05. 2. داده‌ها:

1. مسئله را بیان می کنیم: می‌خواهیم بررسی کنیم آیا بین سه روش درمانی A، B و C در کاهش میزان افسردگی تفاوت معنی‌داری وجود دارد یا خیر در سطح معنی داری 5%. 2. داده‌ها به صورت زیر است

1. Statement: When the mean is computed for individual data, all values in the data set are used. Explanation: True. The mean (average) is found by summing all values and dividing

1. The problem is to understand the concept of a \textbf{statistical vector} in statistics and linear algebra. 2. A statistical vector often represents data points arranged as an o

1. Problem: A vaccine trial with 20 children, 15 developed immunity. (a) Probability at least 15 develop immunity. (b) Expected number and standard deviation.\n 1. (a) Let $X \sim