Statistics Essay Example | Topics and Well Written Essays - 2500 words

Statistics - Essay Example Find your name in the list and make a note of your dataset number. You will use this to access your own datasets for the questions in section B. This project is worth 100% of the final mark Section A: Statistics Quiz Answers to questions in this section require no more than one or two sentences each! 1. Quantitative variables can be discrete or continuous. Explain the difference between discrete data and continuous data, and give one example of each. Answer: A discrete variable can assume only a countable number of values such as number of persons in a family, whereas a continuous variable can assume any numerical value over a certain interval or intervals (uncountable number of values) such as height of a person. 2. A measure of location is a quantity which is ‘typical’ of the data. Give the names of three such measures, and explain (in words, not formulae) how each is found. Answer: The most common measures of central tendency or location used to describe data are; Mod e: This is the most commonly occurring value. Median: The middle value when all the data are placed in order. Mean (Arithmetic Mean): It is the ratio of the sum of the scores to the number of the scores. 3. What is a measure of spread? Give the names of three such measures. ... in figure 1 suggests that median would be a suitable measure of location and interquartile range would be a suitable measure of spread for these data. 5. The probability that a ship has a defective radar is 0.05. The probability that a ship has a defective echo is 0.06. Three in one hundred ships have both a defective echo and a defective radar. Find the probability that a randomly chosen ship has either a defective echo or a defective radar. Answer: P(def. radar) = 0.05 P(def. echo) = 0.06 P(def. radar and def. echo) = 3/100 = 0.03 P (def. radar or def. echo) = P(def. radar) + P(def. echo) – P(def. radar and def. echo) P (def. radar or def. echo) = 0.05 + 0.06 – 0.03 = 0.08 6. Under what conditions might we use a binomial distribution as a probability model for our data? Answer: We use a binomial distribution when following four conditions are satisfied; The number of trials ‘n’ is fixed. Each trial is independent. Each trial represents one of two outcomes ("success" or "failure"). The probability of success ‘p’ is the same for each trial. 7. Under what conditions might we use a normal distribution as a probability model for our data? Answer: The mean, median and mode are equal The graph is symmetrical about the mean (50% above and 50% below) Because 100% of the distribution lies below the curve, the total area below the curve is 100% or 1.  ± 68% of the sample lies within one standard deviation of the mean; 34% above and 34% below  ± 96% within two standard deviations: 48% above and 48% below  ± 99.7% within three standard deviations: 49.85% above and 49.85% below The two ends are asymptotic to the horizontal axis. 8. In hypothesis testing, the p-value can be thought of as the chance of obtaining the observed results, or more extreme results, if the