Unit 3Sections 3-1 & 3-2

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

3-2: 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.

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

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

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.

A B C D

Class Frequencyf

MidpointXm

f*Xm

Finding the Mean: Grouped Data

Section 3-2

Find the mean for the grouped data below:

Class Frequency

fMidpoint

Xm

f*Xm

5.5 – 10.5 1

10.5 – 15.5 2

15.5 – 20.5 3

20.5 – 25.5 5

25.5 – 30.5 4

30.5 – 35.5 3

35.5 – 40.5 2

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

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

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

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

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

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

Finding the Weighted Mean

Section 3-2

A student’s grades are listed below. Find the weighted mean.

Course Credits (w) Grade (X)

English Comp I 3 A (4 points)

Intro to Psych 3 C (2 points)

Biology I 4 B (3 points)

Phys Ed 2 D (1 point)