Math 227 Elementary Statistics, Schemes and Mind Maps of Statistics

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Math 227 Elementary Statistics

Bluman 5th^ edition

CHAPTER 3

Data Description

 Use the techniques of exploratory data

analysis, including boxplots and five-

number summaries to discover various

aspects of data.

Objectives (cont.)

Introduction

 Measures of average are called measures of

central tendency and include the mean,

median , mode, and midrange.

*Loosely stated, the average means the center

of the distribution or the most typical case.

Introduction

 Measures of a specific data value’s relative

position in comparison with other data values

are called measures of position and include

percentiles, deciles, and quartiles.

*Measures of position tells where a specific data

value falls within the data set or its relative

position in comparison with other data value?

Section 3 - 1 Measures of Central Tendency

 A statistic is a characteristic or measure

obtained by using the data values from a

sample.

 A parameter is a characteristic or

measure obtained by using all the data

values for a specific population.

15

I. Mean and Mode

The symbol for a population mean is (mu).

The symbol for a sample mean is (read “x bar”).

The mean is the sum of the values, divided by the total number of values.

x is any data value from the data set. n is the total number of data ( n is called the sample size)

Rounding Rule for the Mean: The mean should be rounded to one more decimal place than occurs in the raw data.

• Example 1: Find the mean of 24, 28,

The procedure for finding the mean for grouped data uses the midpoints

of the classes. The formula for finding the mean of grouped data is

The modal class is the class with the largest frequency.

Example 4:

Thirty automobiles were tested for fuel efficiency (in miles per gallon). Find the mean fuel efficiency and the modal class for the frequency distribution obtained from the thirty automobiles.

Class

Boundaries

Frequency Midpoint

Modal Class =

17.5 – 22.

(highest frequency)

Example 2: Find the median

Reorder: 3, 5, 6, 6, 8, 11, 13, 19, 21, 32

MD = (8 + 11) / 2 = 9.

Midrange is the sum of the lowest and highest values in a data set, divided by 2.

Example 3: Find the midrange of 17, 16, 15, 13, 17, 12, 10

Reorder: 10, 12, 13, 15, 16, 17, 17 MR = (10 + 17) / 2 = 13.

Example 4: The average undergraduate grade point average (GPA) for the top 9 ranked medical schools are listed below.

3.80 3.86 3.83 3.78 3.75 3.75 3.86 3.70 3.

Find (a) the mean, (b) the median, (c) the mode, and (d) the midrange.

(a) Mean

Reorder: 3.70 3.74 3.75 3.75 3.78 3.80 3.83 3.86 3.

III. The Weighted Mean

Weighted Mean – Multiply each value by its corresponding weight and divide the sum of the products by the sum of the weights.

where w 1 , w 2 , ........., wn are the weights and x 1 , x 2 , ........., xn are the values.

Example 1:

An instructor gives four 1-hour exams and one final exam, which counts as two 1-hour exams. Find the student’s overall average if she received 83, 65, 70, and 72 on the 1-hour exams and 78 on the final exam.

Scores (x) Weights (w) W · x