Midterm Review Name: _____________ 1. In an ungrouped frequency distribution of the average age of high school graduates‚ what would be the boundaries for the class of graduates who were reported to be 19 years old? 2. What is the midpoint of the class 4-8 ? 3. Greg wants to construct a frequency distribution for the religious affiliation of the employees at Tim’s Hardware Store. What type of distribution would be best? A) ungrouped B) grouped C) categorical D) cumulative 4. What is the upper
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from a frequency table. The formula for the standard deviation of a set of data is [pic] Recap question A sample of 60 matchboxes gave the following results for the variable x (the number of matches in a box): [pic]. Calculate the mean and standard deviation for x. Introductory example for finding the mean and standard deviation for a table: The table shows the number of children living in a sample of households: |Number of children‚ x |Frequency‚ f
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The Poisson distribution is a discrete distribution. It is often used as a model for the number of events (such as the number of telephone calls at a business‚ number of customers in waiting lines‚ number of defects in a given surface area‚ airplane arrivals‚ or the number of accidents at an intersection) in a specific time period. It is also useful in ecological studies‚ e.g.‚ to model the number of prairie dogs found in a square mile of prairie. The major difference between Poisson and Binomial
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Descriptive statistics information Descriptive statistics organize‚ summarize‚ and communicate a group of numerical observations and describe large amounts of data in a single number or in just a few numbers Inferential statistics Use samples to draw conclusions about a population Inferential statistical use sample data to make general estimates about the larger population‚ and infer or make an intelligence guess about‚ the population Sample: a set of observations drawn from the population
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as : frequency and relative frequency distributions‚ bar graphs and pie charts. 2. Learn how to construct and interpret tabular summarization procedures for quantitative data such as: frequency and relative frequency distributions‚ cumulative frequency and cumulative relative frequency distributions. 3. Learn how to construct a dot plot‚ a histogram‚ and an ogive as graphical summaries of quantitative data. 4. Learn how the shape of a data distribution is revealed
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Mathematics): Survival distributions Age-at-death random variable T0 – age-at-death (lifetime for newborn) random variable To completely determine the distribution of T0 ‚ we may use (for t ≥ 0)‚ (1) (cumulative) distribution function: F0 (t) = Pr(T0 ≤ t) (2) survival function: s0 (t) = 1 − F0 (t) = Pr(T0 > t) (3) probability density function: f0 (t) = F0 (t) = (4) force of mortality: µ0 (t) = d F0 (t) dt f0 (t) −s0 (t) = 1 − F0 (t) s0 (t) Requirements: (1) For distribution function‚
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class was born in August. Answer: Number of students born in the month of August = 6 Total number of students = 40 Question 4: Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcome 3 heads 2 heads 1 head No head Frequency 23 72 77 28 If the three coins are simultaneously tossed again‚ compute the probability of 2 heads coming up. Answer: Number of times 2 heads come up = 72 Cbse-spot.blogspot.com
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Recognize the difference between grouped and ungrouped data Construct a frequency distribution Construct a histogram‚ a frequency polygon‚ an ogive‚ a pie chart‚ Ungrouped data have not been summarized in any way • are also called raw data • Grouped data • have been organized into a frequency distribution 42 26 32 34 57 30 58 37 50 30 53 40 30 47 49 50 40 32 31 40 52 28 23 35 25 30 36 32 26 50 55 30 58 64 52 49 33 43 46 32 61 31 30 40
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expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is ‚ formally defined by Variance - The variance of a discrete random variable X measures the spread‚ or variability‚ of the distribution‚ and is defined by The standard deviation is the square root of the variance. Expectation - The expected value (or mean) of X‚ where X is a discrete random variable‚ is a weighted average of the possible values that X can take‚ each value
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categories. It is important that data are organized to identify important characteristics. One way of rearranging data is through the stem-and-leaf plot. A stem-and-leaf plot is a display that organizes a set of data to show both its shape and its distribution. Each data value is split into a “stem” and “leaf”. The leaf is usually the last digit of the number‚ and the other digits to the left of the leaf form the stem. Example 2: The stem-and-leaf plot for the ages of farmer borrowers interviewed:
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