📊 statistics
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.
Mean And Mode
1. **State the problem:** We have grouped data of student ages and their frequencies. We need to calculate the mean age and analyze the histogram to find the modal age.
2. **Calcul
Sampling Sizes
1. **Advantages and Disadvantages of Sampling Methods:**
**Probability Sampling Methods:**
Standard Normal Areas
1. **Problem Statement:**
Find the area of the standard normal distribution between z = -0.67 and z = 0 (Check Your Progress 3).
Zoo Survey
1. **State the problem:** There are 85,740 people surveyed, and 11/30 of them go to the zoo more than twice a year. We need to find how many people that is and round the answer to
Normal Distribution Tomatoes
1. **Problem statement:**
A vegetable distributor has tomato weights normally distributed with mean $\mu = 0.61$ lb and standard deviation $\sigma = 0.15$ lb.
Statistical Indices
1. সমস্যার বর্ণনা: আমাদের কাছে প্রাণী সংখ্যার শ্রেণীবিন্যাস এবং জনসংখ্যার তথ্য দেওয়া হয়েছে।
প্রতিটি শ্রেণীর (৩০-৪০, ৪০-৫০, ..., ৯০-১০০) জনসংখ্যা আছে (৪, ৬, ৮, ১২, ৯, ৭, ৪)।
Cluster Variance
1. **Problem Statement:**
Calculate the variance between clusters $v_b$ using the given formula:
Variance Within Cluster
1. Masalah: Hitung varians dalam klaster ($v_w$) dari dataset titik-titik (1,1), (3,1), (1,3), (3,3), (7,7), dan (9,9).
2. Langkah pertama adalah menetapkan klaster dan jumlah data
Frequency Tree
1. State the problem: There are 70 students in total.
- 44 brought a packed lunch.
Graph Interpretation
1. The problem asks us to draw three graphs using the data from Q6: (a) a Histogram, (b) a Frequency Polygon, and (c) an Ogive curve, and then estimate the median wage from the ogi
Bent Rods Distribution
1. **Stating the problem:**
We have a random variable $X$ denoting the number of bent rods in a sample of 400 rods. Each rod has a 1.2% chance of being bent.
Percentage Distribution
1. **State the problem:** We have income groups in thousands (n000) and the number of families in each group as follows:
Income (n000): 5–10, 10–15, 15–20, 20–25, 25–30
Marks Frequency Range
1. **State the problem:** We have marks out of 20 for 10 students: 10, 8, 15, 12, 7, 18, 10, 12, 14, 9.
We need to prepare a frequency table showing each mark and the number of stu
Rainfall Data Sheet
1. The problem asks to prepare a data sheet suitable for tabulation to record monthly rainfall from 10 rain-gauges in different zones.
2. To structure the raw data, we create a tab
Sampling Electricity
1. The problem is to design a sampling plan to study the monthly electricity consumption of 100 households in a city and explain data collection methods.
2. Sampling plan: Use simp
Sampling Probabilities
1. **Problem 1: TV Viewing Hours**
Given:
Mixing Index
1. **Nyatakan masalahnya:** Kita memiliki dua set data komposisi % yeast dari 10 sampel pada dua waktu pencampuran, yaitu 5 menit dan 10 menit.
2. **Hitung nilai rata-rata (mean) d
Normal Area Left
1. The problem asks to find the area under the standard normal distribution curve to the left of $z = 2.25$.
2. The standard normal distribution has a mean of 0 and standard deviat
Normal Distribution
1. The normal distribution curve is typically associated with probability and statistics, particularly the bell-shaped curve representing Gaussian distribution.
2. To determine if
Gmat Probability
1. State the problem.
Most GMAT scores are normally distributed with mean $527$ and standard deviation $112$.
Gmat Score Probability
1. **State the problem:** We want to find the probability that a person scores above 500 on the GMAT, given that scores are normally distributed with mean $\mu = 527$ and standard