AP STATISTICS: Summer Math Packet

Transcription

1 Name AP STATISTICS: Summer Math Packet DIRECTIONS: Complete all problems on this packet. Packet due by the end of the first week of classes. Attach additional paper if needed. Calculator may be used. 1. Look at the frequency table above. Identify in general what s wrong with this grouping scheme then cite two example resulting from this problem. 2. The frequency distribution table for the housing type is as follows: a) What is the total number of observations (total frequency)? n = b) What is the sum of the relative frequency? c) Interpret the meaning of the frequency for Apartment. d) Interpret the relative frequency for Apartment.

2 3. Let X1 = 8, X2 = 9, and X3 = 5. Using these values, show by example why Standard deviation is used as a measurement of distance between any measurement and the mean of the data set. For example, a measurement can be described as being so many standard deviations above or below the mean. A standard deviation of 0 indicates no change in the measurements. For example, if a student scores 8, 8, 8, and 8 on 4 quizzes, then the standard deviation of the scores is 0. A larger standard deviation indicates a larger spread among the measurements. 4. Consider the two student s quiz grades below. Use the information about standard deviation and decide which student would have a larger standard deviation. Student A: 4, 5, 6, 7, 8, 8, 8, 9, 9, 10 Student B: 5, 5, 6, 6, 6, 7, 7, 7, 8 5. Scale the x-axis from 4 to 10 in units of one. Construct parallel box plots of the student data above using the same scale.

3 Standardized scores or z-scores: Standardized scores, commonly known as z-scores, are independent of the units in which the data values are measured. Therefore, they are useful when comparing observations from different data sets measured on different scales. They are computed as: z score = measurement mean standard deviation A z-score gives the distance between the measurement and the mean in terms of the number of standard deviations. A negative z-score indicates that the measurement is smaller than the mean; a positive z-score indicates that the measurement is larger than the mean. NOTE: standard deviation is a measurement of the spread of a data set, we will learn more about this measurement later. Example: Suppose a teacher gave her students a test. The class average for student A was 74 and the standard deviation was 6. The class average for student B was 76 with a standard deviation of 5. Suppose student A got an 88 and student B got a 89. The z-score for student A is: z-score = = a) Find the z-score for student B (show work): b) Compare z-scores for student A and for student B. Which student did better relative to their class? Why? 7. A small used car dealer wanted to get an idea of how many cars her dealership sells per day. Listed below is the number of cars per day sold over a two-week period: Number of cars sold Find: a) The mean number of cars sold per day (round to 2 significant digits) b) The range of cars sold per day c) The median number of cars sold per day d) The first and third quartiles of the number of cars sold per day, e) The interquartile range of the number of cars sold per day

4 8. A random sample of 10 office assistants hired within the last six months was selected from a large company. For each selected office assistant, his or her experience (in months) at the time of hire and starting salary (in $1,000) were recorded and displayed in the scatterplot below. The equation of the least squares regression line (or line of best fit) is: salary = (experience) a) What is the slope of the least squares regression line? b) Interpret the meaning of the slope. c) Describe the relationship between experience and salary.

5 Example of a binomial distribution: Properties are described below to justify that this experiment is a binomial distribution: There are 20 repeated trials All trials are identical There are only two possible outcomes, an item is defective or not-defective We don t know the probability of success (or failure) but assume it is constant Justify that the following experiments have a binomial distribution by identifying each property: