Frequency and Probability Distribution Flashcards

Question

What are the steps to constructing a grouped frequency distribution table?

Answer 1

1. Finding the range. Range = (highest data value minus the lowest data value)+ 1 2. Determine the interval width (i) - ideally between 5 and 20 - try to find a whole number - he will tell us how many intervals (number of groups the data is divided into) he wants so no worries. formula: i = range/number of class intervals **Attention class intervals have to be continuous 3. Identify interval midpoints (point au milieu de la classe d'intervalle): Formula: Midpoint(i) = minimum + ((max-min)/2) 4. Identify real limits of each class interval: real limits(i) = midpoint ± (width/2) 5. Count the raw scores and add them up to determine the frequencies. 6. Figure the relative frequency (p) for each interval relative f = f/n 7. Figure the cumulative frequency distribution for each class interval - indicates the number of scores that fell below the upper real limits of the desired data value 8. Figure the cumulative proportion distribution of each class interval.

Answer 2

Midpoint: It gives a single number to represent the whole interval, which makes calculations (like averages) and graphs simpler. Real limits: They make sure there's no overlap or gaps between intervals and help include borderline values properly, especially for continuous data. Borderline values" are numbers that fall exactly at the boundary between two class intervals in a frequency distribution. For example: If your class intervals are 10–14 and 15–19, the values 14 and 15 are borderline values because they mark the division between these two intervals.

Answer 3

-They are kind of a bar chart (bars are put right next to each other because we are graphing continuous data, interval or ratio). not independent data like with a bar graph. -Height of each bar corresponds to the frequency of each value or interval in the frequency distribution table

Answer 4

To provide information about the shape of the distribution.

Answer 5

A curve is symmetrical if when folded in half the two sides coincide. If a curve is not symmetrical it is skewed In a positively skewed curve most of the scores occur at the lower values of the horizontal axis, and the curve tails (like think an actual tail of an animal) off toward the higher end; may reflect a floor effect In a negatively skewed curve most of the scores occur at the higher values of the horizontal axis, and the curve tails off toward the lower end; may reflect a ceiling effect

Answer 6

* Simultaneously displays the rank order and the shape of the distribution data. * The display is created by rank ordering the leading digit(s) of each data value to the left of the vertical line (stem), and recording the last digit(s) for each data value to the right of the vertical line (leaf) * 2 primary advantages of the stem and leaf display over the histogram 1) Easier to construct by hand 2) Provides more information because it shows the actual data

Answer 7

It is a numerical measure of the chances that an event will occur. * Probabilities can be used as a measure of uncertainties associated with events

Answer 8

0: the event is very unlikely to occur. 0.5: the occurrence of the event is just as likely as it is unlikely. 1. the event is almost certain to occur.

Answer 9

from 0 to 1. There are no negative values.

Answer 10

In a statistical experiment, the outcomes are not completely predictable because they are based on probability. Even though the experiment is repeated in exactly the same way, an entirely different outcome may occur. Ex: coin flip

Answer 11

Random experiments

Answer 12

An experiment (trial) is any process that generates well-defined outcomes * On any single repetition of an experiment, one and only one of the possible experimental outcomes will occur ex.: experiment - toss a coin experiment outcomes: head, tail. experiment- play a football game experimental outcomes: win, lose, tie

Answer 13

The sample space for an experiment is the set of all experimental outcomes. * An experimental outcome is also called a sample point to identify it as an element of the sample space. ex: toss a coin S (sample space) = [Head (sample point), tail]

Answer 14

1. The probability assigned to each experimental outcome must be between 0 and 1, inclusively. 0

Answer 15

The classical method, the relative frequency method and the subjective method.

Answer 16

Assigning probabilities based on the assumption of equally likely outcomes Example: Rolling a Die If an experiment has n possible outcomes, the classical method would assign a probability of 1/n to each outcome. Experiment: Rolling a die Sample space: S={1,2,3,4,5,6} Probabilities: Each sample point has a 1/6 chance of occurring

Answer 17

Assigning probabilities based on experimentation or historical data. Example: Lucas Tool Rental Lucas Tool Rental would like to assign probabilities to the number of car polishers it rents each day. Office records show the following frequencies of daily rentals for the last 40 days. Each probability assignment is given by dividing the frequency (number of days) by the total frequency (total number of days). Basically same as relative frequency. f 0 polishers were rented for 4 days out of the 40 days, then the probability of no polishers being rented on a given day is 0.10 (4 days/40 - 0 polishers were rented each day for those 4 days out of 40)

Answer 18

The subjective method of assigning probabilities means using judgment to estimate the likelihood of an outcome, especially when historical data isn't enough or the situation is changing quickly. It involves considering available data, as well as personal experience and intuition. Ultimately, the probability reflects how confident you are that a specific outcome will happen. Gut felling type of thing. Often, the best estimates come from combining both the estimates from the classical or relative frequency approach with the subjective estimate. Example: Estimating the Probability of a Product Selling Out Suppose you work for a company that sells a limited edition product, and you want to estimate the probability that it will sell out by the end of the week. Relative Frequency Estimate: Based on historical data, you know that similar products have sold out 80% of the time over the past few months. This is a data-driven estimate. Subjective Estimate: However, this time, the economic conditions have changed (e.g., there’s a new competitor), and you feel there’s a 50% chance that the product might sell out, based on your knowledge of the current market trends and consumer behavior. Combining Both Estimates: You could combine the two estimates, perhaps by averaging them or weighing them based on how confident you are in each approach: Combined Probability: (80%+50%) / 2 = 65% Alternatively, if you trust the historical data more, you could weigh it higher, such as: Combined Probability This gives you a 74% chance of selling out the product.

Answer 19

A collection of sample points. example: Event A = days on which 3 or more polishers were rented. A = {(3),(4)} ** basically saying: on the days where 3 polishers were rented and on the days where 4 polishers were rented, that is what we are focusing on, because we want to track the days where the number of polisher rented is 3 or more. The number of polishers rented IS THE EXPERIMENTAL OUTCOME!!!**

Answer 20

1. The probability of any event is equal to the sum of the probabilities of the sample points in the event. If we can identify all the sample points of an experiment and assign a probability to each, we can compute the probability of an event. What is the case for : Event A = days on which 3 or more polishers were rented A = {(3),(4)} P(A) - meaning probability de event A = P(3) + P(4) = 0.25+0.05 = 0.30 2. The probability of any event can also be found by dividing the number of successful experimental outcomes (Nsuccess) by the total number of experimental outcomes (NSE) Example with luca tool rentals: Event A = Days on which 3 or more polishers were rented P(A) = Nsuccess/ N(SE) = 10 + 2 / 40 = 0.30

Answer 21

Mutually exclusive events are events that cannot co-occur. Example rolling a 2 and a 3 on a die. Events are independent if the occurrence of one does not affect the probability of the other occurring. ex: rolling a dice twice, the outcome of the first roll and second roll have no effect on each other.