1. Unit 3 Sections 3-1 & 3-2

2. What we will be able to do throughout this chapter…  Use statistical methods to summarize data  The most familiar method is using “averages”. Also known as measures of central tendencies.  Mean, Median, Mode, and Midrange  Measures of variation or measures of dispersion  Range, Variance, and Standard Deviation  Measures of position  Percentiles, Deciles and Quartiles Section 3-1

3. 3-2: Measures of Central Tendency  Statistic – a characteristic or measure obtained by using the data values from a sample.  Parameter – a characteristic or measure obtained by using all the data values from a specific population.  NOTE: General Rounding Rule  In statistics, rounding takes place when all computations are completed.

4.  Mean – the sum of the values, divided by the total number of values.  Also known as the arithmetic average.  Sample mean:  Population mean:  Rules for a Rounding a Mean:  If the original data is given in whole numbers, we would round the mean to 1 decimal place.  If the original data is given to one decimal place, we would round the mean to 2 decimal places. Section 3-2

5. Finding the Mean Section 3-2  Determine the mean of the following data representing the number of days off for individuals from nine different countries. 20, 26, 40, 36, 23, 42, 35, 24, 30

6. Finding the Mean for Grouped Data Section 3-2  Make a table as shown  Find the midpoints of each class and place them in column C.  Multiply the frequency by the midpoint for each class, and place the product in column D.  Find the sum of column D.  Divide the sum of column D by the sum of the frequencies obtained in column B. ABCD ClassFrequency f Midpoint X m f*X m

7. Finding the Mean: Grouped Data Section 3-2  Find the mean for the grouped data below: ClassFrequency f Midpoint X m f* X m 5.5 – 10.51 10.5 – 15.52 15.5 – 20.53 20.5 – 25.55 25.5 – 30.54 30.5 – 35.53 35.5 – 40.52

8.  Median – the midpoint of the data array.  Think of it as the middle number.  Notation: MD  Steps for finding the median:  Place the numbers in order.  Select the middle point. If there are two numbers that fall in the middle, add the two values together and divide by two Section 3-2

9. Finding the Median Section 3-2  Find the median for each data set: 1, 3, 4, 2, 3, 5, 1 684, 764, 656, 702, 856, 1133, 1132, 1303

10.  Mode – the value that occurs most often in a data set.  Unimodal – a data set that has only one value that occurs the most.  Bimodal – a data set that has two values that occur with the same greatest frequency.  Multimodal – a data set that has more than two values that occur with the same greatest frequency.  No Mode – a data set where no values occur more than once.  Modal Class – the mode for grouped data. Section 3-2

11. Finding the Mode Section 3-2  The following data represents the duration (in days) of U.S. Space Shuttle voyages for the years 1992-1994. Find the mode 8, 9, 9, 14, 8, 8, 10, 7, 6, 9, 7, 8, 10, 14, 11, 8, 14, 11

12.  Midrange – the sum of the lowest and highest values in a data set, divided by two.  Considered a rough estimate of the average.  Notation: MR Example - Suppose the number of water- line breaks was as follows: 2, 3, 6, 16, 4, and 1 Find the midrange. Section 3-2

13.  Weighted Mean – a type of mean that considers and additional factor.  Determined by…  Multiplying each value by its corresponding weight.  Sum the products together.  Divide the sums by the total value of the weights.  A common situation where weighted means are used is calculating grade point averages. Section 3-2

14. Finding the Weighted Mean Section 3-2  A student’s grades are listed below. Find the weighted mean. CourseCredits (w)Grade (X) English Comp I3A (4 points) Intro to Psych3C (2 points) Biology I4B (3 points) Phys Ed2D (1 point)