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Definitions:
- Be able to classify variables as either
(a) Population vs. Sample (b) Quantitative vs. Qualitative (c) Discrete vs. Continuous
- Be able to take raw data and make a frequency distribution table and a histogram Ex : The ages of 20 children are given as followed:
(a) Create a frequency distribution table (b) Create a histogram for the data
- Finding mean, median and mode for ungrouped data
(a) Mean and Variance for Population data :
μ =
Σx N
σ^2 =
Σx^2 − (^) N^1 (Σx)^2 N
(b) Mean and Variance for Sample data :
x = Σx n
s^2 =
Σx^2 − (^) n^1 (Σx)^2 n − 1
- Finding mean and standard deviation for grouped data.
Commuting Time (in minutes) f m mf m^2 f 0 to less than 10 3 10 to less than 20 5 20 to less than 30 8 30 to less than 40 11 40 to less than 50 7
- Stem and Leaf displays. Given raw data, make a stem and leaf display. Also, given a stem and leaf display, find the raw data. Example : Create a stem and leaf display for the following data:
Example : The following is a stem and leaf display. Write the data set that is represented by the display
- Chebyshev’s Theorem and Empirical Rule
(a) Chebyshev’s Theorem : For any k ≥ 1, at least
k^2 of the values are within k standard deviations of the mean. (b) Empirical Rule : For a data set with a bell-shaped distribution
- Approximately 68 percent of the data lie within 1 standard de- viation of the mean.
- Approximately 95 percent of the data lie within 2 standard de- viations of the mean.
- Approximately 99.7 percent of the data lie within 3 standard deviations of the mean.
- Probability : Experiments, Outcomes, Sample Spaces, Conditional Prob- ability, Intersections and Unions of Events Example :
A A Total B 3 4 B 6 8 Total
(a) Find P (A), P (B), P (B), P (A ∩ B), P (A | B), P (A | B), P (A ∪ B). (b) Are the events A and B independent? (c) Are the events A and B mutually exclusive?
Example : Toss a coin three times. Let A be the event that there was at least one head, and let B be the event there was exactly one tail.
(a) Find the sample space for this experiment.
