Normal Distribution It is important because of Central Limit Theorem (CTL)‚ the CTL said that Sum up a lot of i.i.d random variables the shape of the distribution will looks like Normal. Normal P.D.F Now we want to find c This integral has been proved that it cannot have close form solution. However‚ someone gives an idea that looks stupid but actually very brilliant by multiply two of them. reminds the function of circle which we can replace them to polar coordinate Thus Mean
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Standard deviation can be difficult to interpret as a single number on its own. Basically‚ a small standard deviation means that the values in a statistical data set are close to the mean of the data set‚ on average‚ and a large standard deviation means that the values in the data set are farther away from the mean‚ on average. The standard deviation measures how concentrated the data are around the mean; the more concentrated‚ the smaller the standard deviation. A small standard deviation can
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What is the mean age of this sample? What is the standard deviation? The mean age is 47.5 years old. The standard deviation is 10.74832 years. http://www.calculator.net/standard-deviation-calculator.html Sample Standard Deviation‚ s: 10.748316881702 Sample Standard Variance‚ s2 115.52631578947 Total Numbers‚ N 20 Sum: 950 Mean (Average): 47.5 Population Standard Deviation‚ σ 10.476163419878 Population Standard Variance‚ σ2 109.75 If it follows the normal distribution The 68.3%
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S1 Jan 2001 1) The students in a class were each asked to write down how many CDs they owned. The student with the least number of CDs had 14 and all but one of the others owned 60 or fewer. The remaining student owned 65. The quartiles for the class were 30‚ 34 and 42 respectively. Outliers are defined to be any values outside the limits of 1.5(Q3 – Q1) below the lower quartile or above the upper quartile. On graph paper draw a box plot to represent these data‚ indicating clearly any outliers
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In the following multiple choice questions‚ circle the correct answer. 1. Which of the following provides a measure of central location for the data? a. standard deviation b. mean c. variance d. range Answer: b 2. A numerical value used as a summary measure for a sample‚ such as sample mean‚ is known as a a. population parameter b. sample parameter c. sample statistic d. population mean Answer: c 3. Since the population size is always
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that‚ as the score of one increases‚ the score of the other increases. (Points : 1) | True False | 4. A result that is probably not attributable to chance is: (Points : 1) | Type I error Type II error Statistical significance In the semi-quartile range | 5. A score that is likely to fall into the middle 68% of scores of a normal distribution will fall inside these values: (Points : 1) | . +/- 3 standard deviations +/-
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Marks: 1 Assume that X has a normal distribution‚ and find the indicated probability. The mean is μ = 60.0 and the standard deviation is σ = 4.0. Find the probability that X is less than 53.0. Choose one answer. a. 0.5589 b. 0.0401 c. 0.9599 d. 0.0802 Question2 Marks: 1 Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation. Assume that the population has a normal distribution. Weights of eggs: 95% confidence;
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for this question. 85 72 64 65 98 78 75 76 82 80 61 92 72 58 65 74 92 85 74 76 77 77 62 68 68 54 62 76 73 85 88 91 99 82 80 74 76 77 70 60 A. Construct two different graphs of these data B. Calculate the five-number summary and the mean and standard deviation of the data. C. Describe the distribution of the data‚ citing both the plots and the summary statistics found in questions 1 and 2. AP Statistics Exam Review Topic II: Normal Distribution [pic] [pic] [pic] [pic] [pic] [pic]
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Chapter 13: Chi-Square Applications SHORT ANSWER 1. When samples of size n are drawn from a normal population‚ the chi-square distribution is the sampling distribution of = ____________________‚ where s2 and are the sample and population variances‚ respectively. ANS: PTS: 1 OBJ: Section 13.2 2. Find the chi-square value for each of the right-tail areas below‚ given that the degrees of freedom are 7: A) 0.95 ____________________ B) 0.01 ____________________ C) 0.025 ____________________
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Standard deviation is the square root of the variance (Gravetter & Wallnau‚ 2013). It uses the mean of the distribution as a reference point and measures variability by considering the distance of each score from the mean. It is important to know the standard deviation for a given sample because it gives a measure of the standard‚ or average‚ range from the mean‚ and specifies if the scores are grouped closely around the mean or are widely scattered (Gravetter & Wallnau‚ 2013). The standard deviation
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