Statistics

Population Data: Including data from ALL people or items with the characteristic one wishes to understand. Sample Data: Utilizing a set of data collected and/or selected from a statistical population by a defined procedure.

Can you think of examples? When would you use population data? EX: When would you use sample data? EX:

5 main methods: Random Sampling Systematic Sampling Stratified Sampling Cluster Sampling Convenience Sampling

The “pick a name out of the hat” technique Random number table Random number generator Hawkes and Marsh (2004)

All data is sequentially numbered Every nth piece of data is chosen Hawkes and Marsh (2004)

Data is divided into subgroups (strata) Strata are based specific characteristic Age Education level Etc. Use random sampling within each strata Hawkes and Marsh (2004)

Data is divided into clusters Usually geographic Random sampling used to choose clusters All data used from selected clusters Hawkes and Marsh (2004)

Data is chosen based on convenience BE WARY OF BIAS! Hawkes and Marsh (2004)

Bias means how far from the true value the estimated value is. If a value has zero bias it is called unbiased. Why is this important in statistical studies?

Selection Bias Omitted- Variable Bias Funding Bias Reporting/ Response Bias Analytical Bias Exclusion Bias Can you think of others?

In a class of 18 students, 6 are chosen for an assignment Sampling TypeExample RandomPull 6 names out of a hat SystematicSelecting every 3 rd student StratifiedDivide the class into 2 equal age groups. Randomly choose 3 from each group ClusterDivide the class into 6 groups of 3 students each. Randomly choose 2 groups ConvenienceTake the 6 students closest to the teacher

Determine average student age Sample of 10 students Ages of 50 statistics students

Random number generator Data Point Location Corresponding Data Value Mean25.1

Take every data point Data Point Location Corresponding Data Value Mean20.8

Take the first 10 data points Data Point Location Corresponding Data Value Mean22.5

In a group of two or three, create a list of at least 3 pros and 3 cons for each type of sampling. In the same group, create a list of when you may use each type of sampling and for what reason. As a group determine which type of sampling is overall the best, and which is overall the easiest.

Measures of Central Tendency: Values that describe the center of distribution. The mean, median, and mode are 3 measures of central tendency. Mean: A measure of central tendency that is determined by dividing the sum of all values in a data set by the number of values. Frequency Distribution Table: A table that lists a group of data values, as well as the number of times each value appears in the data set. Outliers: Extreme values in a data set.

µ pronounced ‘mu’ Symbols which represents the mean population ∑ Symbol which means ‘the sum of’– represents the addition of numbers N Symbol which represents the number of data values of a given population

Mark operates a donut business which has 8 employees. There ages are as follows: 55, 63, 34, 59, 29, 46, 51, 41. Find the mean age of the workers. Which will we use? Population or Sample? Why?

The selling prices for the last 10 houses sold in a small town are listed below: $125,000$142,000$129,500 $89,500$105,000 $144,000$168,300$96,000 $182,300$212,000 Calculate the mean selling price of the last 10 homes that were sold. Is this a population or sample?

60 students were asked how many books they had read over the past 12 months. The results are listed in the frequency distribution table below. Calculate the mean number of books read by each student BooksFrequency

The following data shows the heights in centimeters of a group of 10 th grade students. Organize the data in a frequency distribution table and calculate the mean height of the students

The mean can be affected by extreme values or outliers. Example: If you are employed by a company that paid all of its employees a salary between $60,000 and $70,000 you could estimate the mean salary to be about $65,000. However if you add the $150,000 of the CEO then the mean would increase greatly.

To calculate mean of a sample in the calculator: STAT  Edit  Put in your data into L1  2 nd Quit STAT  CALC  1-Var Stats  Enter  Enter

Use technology to determine the mean of the following set of numbers: 24, 25, 25, 25, 26, 26, 27, 27, 28, 28, 31, 32

In Tim’s school, there are 25 teachers. Each teacher travels to school every morning in his or her own car. The distribution of the driving times (in minutes) from home to school for the teachers is shown in the table below: Driving TimesNumber of teachers 0 to 10 minutes3 10 to 20 minutes10 20 to 30 minutes6 30 to 40 minutes4 40 to 50 minutes2

The following table shows the frequency distribution of the number of hours spent per week texting messages on a cell phone by th grade students at a local high school. Calculate the mean number of hours per week spent texting. Time per Week (hours)Number of Students 0 to less than 58 5 to less than to less than to less than to less than to less than 305

Median: The value of the middle term in a set of organized data. Cumulative Frequency: The sum of the frequencies up to and including that frequency.

Find the median of the following set of data: 12, 2, 16, 8, 14, 10, 6 First organize the data from least to greatest. Then find the middle number. When there are two middle numbers, take the two add them together and divide by 2.

Find the median of the following data: 7, 9, 3, 4, 11, 1, 8, 6, 1, 4

The amount of money spent by each of 15 high school girls for a prom dress is shown below. Find the median price of a prom dress. $250$175$325$195 $450$300$275$350 $425$150$375$300 $400$225$360

To calculate mean of a sample in the calculator: STAT  Edit  Put in your data into L1  2 nd Quit STAT  CALC  1-Var Stats  Enter  Enter Scroll down to the Med button and this gives you the median of the data.

The local police department spent the holiday weekend ticketing drivers who were speeding. 50 locations within the state were targeted. The number of tickets issued druing the weekend in each of the locations is shown below. What is the median number of speeding tickets issued?

Mode: The value or values that occur with the greatest frequency in a data set. Unimodal: The term used to describe the distribution of a data set that has only one mode. Bimodal: The term used to describe the distribution of a data set that has 2 modes. Multimodal: The term used to describe the distribution of a data set that has more than two modes.

The posted speed limit along a busy highway is 65 miles per hour. The following values represent the speeds (in mph) of 10 cars that were stopped for violating the speed limit. Find the mode Is this unimodal, bimodal, or multimodal?

The ages of 12 randomly selected customers at a local coffee shop are listed below. What is the mode of the ages? Is this unimodal, bimodal, or multimodal?

QUESTIONS???