Chapter 7

 

Section 7.1:  Averages, Medians, and Modes

A statistic is a number or numbers describing particular data.  The most common ways of finding the center point is with the use of finding the average or the median.  The average is found by adding all of the numbers and dividing by the number of terms.  For an example of this consider the set of test scores 6, 5, 9, 9, 6.  The sum of the terms is 35 and the number of terms is 5.  The average is 6+5+9+9+6 / 5 = 35/5 = 7.  An average is also known as an ARITMETIC MEAN.  Another example would be to find a Grade Point Average (GPA) for Kay with her grades being A, C, C, B, B with the following grade table:

          A = 4

          B = 3

          C = 2

          D = 1

And   F = 0

Translating Kay’s grades to numbers using the above table, Kay’s grades look like:  4, 2, 2, 3, 3.  Her average is 4+2+2+3+3/5 = 14/5 = 2.8.  Looking at the above table, Kay’s grades are closer to a B that a C which implies that Kay is getting a B-.

Next is the median, it is determined by putting the numbers in ascending order and in the case of an odd amount of terms, it is the middle term and in the case of an even number of terms, it is the average of the two middle terms.  For an odd example of this, consider the sequence 7, 4, 10, 10, 9.  Putting the sequence in ascending order I get 4, 7, 9, 10, 10 and the middle term is a 9 so therefore the median is 9, even though the average is

4+7+10+10+9/5 = 40/5 = 8 so be advised that the median may not be the average.  Now for the even number of terms consider is 7, 3, 5, 5, 7, 6.  Rearranged in ascending order it becomes 3, 5, 5, 6, 7, 7.  the median is the average of 5, 6 since they are the middle terms, which becomes 5+6/2 = 11/2 = 5 1/2 which is close to the average = 32/6 = 5 1/3. 

The mode is the number that occurs most.  If more than one number occurs the same number of times, then there is no mode.  Consider the sequence

3, 5, 5, 6, 7, 7.  Because 5 and 7 both occur the maximum number of times, there is no mode, but the sequence 3, 5, 5, 6, 7, 7, 7 has a mode of 7 because 7 occurs the maximum number of times.  Consider the number 8, it is not considered a sequence because there must more than one number to be considered a sequence, but if it were, 8 would be the mode.

 

Section 7.2:  Tables and Pictographs

An example of a table is:

page 456 of Basic Mathematics 9th Edition by Marvin L. Bittinger

Some examples of questions that could be asked of this table are:

How long is a year on Pluto?  A revolution of a planet constitutes a year to that planet.  According to the table a revolution of Pluto occurs every

243.53 years therefore 1 year in Pluto occurs every 248.53 years here on earth.

How far is Mercury from the sun?  According to the table Mercury is 35,983,000 miles from the sun.

What is the largest planet?  The table says that Jupiter is.

Those are examples of how to use a table.  An example of a pictograph is:

page 458 of Basic Mathematics 9th Edition by Marvin L. Bittinger

Examples of how to use a pictograph are:

According to the pictograph, which year will the population be the most?  2070

According to the pictograph, which year will the population be the least?  1650

Approximately how many people are in the world in 1999?  6 billion people.

Section 7.3:  Bar Graphs and Line Graphs

An example of a bar graph is:

page 461 of Basic Mathematics 9th Edition by Marvin L. Bittinger

Some questions that could be asked using this are:

Which product consists of the most amount of fat?  Big Bacon Classic

Which product consists of the least amount of fat?  Spicy Chicken

What product has 20g of fat?  Both the Chicken Club and the Single with

Everything.

An example of a line graph would be:

page 465 of Basic Mathematics 9th Edition by Marvin L. Bittinger

Some questions that could occur using this data are:

Which time of loan could yield a payment of $1000 per month?  20 years

 

Approximately how much would be paid per month on a 30 year loan? 

About $850.00 a month.

Section 7.4 Circle Graphs

The following is an example of a circle graph:

page 473 of Basic Mathematics 9th Edition by Marvin L. Bittinger

The following could be asked here:

How much in percentage would be in food?  36%

What is 3% of the total cost?  The price of the dog.

For further examples see page 473.

 

Chapter 8

 

Section 8.1 Linear Measures: American Units

The American units of measure are:

12 inches (in) = 1 foot (ft)

36 inches (in) = 1 yard (yd)

63360 inches (in) = 1 mile (mi)

3 feet (ft) = 1 yard (yd)

5280 feet (ft) = 1 mile (mi)

1760 yards (yd) = 1 mile (mi)

Section 8.2 Linear Measures: The Metric System

1 meter ≈ (or approximately) 1.1 yards

prefixes or what to multiply by:

kilo = 1000

hecto = 100

deka = 10

deci = 1/10 = 0.1

centi = 1/100 = 0.01

milli = 1/1000 = 0.001

then by using the prefixes, 1 kilometer = 1000 meters = 100,000 centimeters.

The metric units are:

1 kilometer (km) =

10 hectometer (hm) =

100 dekameter (dam) =

1000 meters (m) =

10,000 decimeters (dm) =

100,000 centimeters (cm) =

1,000,000 millimeters (mm)

Section 8.3 Converting between American Units and Metric Units

The conversion table is as follows:

1 in                        = 2.54 cm

1 ft                        = 0.305 m

1 yd                       = 0.914 m

1 mi                       = 1.609 km

0.621 mi                = 1 km

1.094 yd                = 1 m

3.281 ft                  = 1 m

39.370 in                = 1 m

0.394 in                 = 1 cm

Section 8.4 Weight and Mass; Medical Applications

American units of weight:

1 pound (lb)          = 16 ounces (oz)

1 ton (T)               = 2000 pounds (lb)

Metric units of weight:

1 metric ton (t)                 = 1000 kilograms (kg)

1 kilogram (kg)                =

10 hectogram (hg)            =

100 dekagrams (dag)       =

1000 grams (g)                =

10,000 decigrams (dg)     =

100,000 centigrams (cg)   =

1,000,000 milligrams (mg)

1 microgram (mcg)          = 1/1,000,000 g = 0.000001 g

Section 8.5 Capacity; Medical Applications

American units of capacity:

1 gallon (gal)          = 4 quarts (qt)

1 quart (qt)            = 2 pints (pt)

1 pint (pt)              = 2 cups

1 pint (pt)              = 16 fluid ounces (fl oz)

1 cup                    = 8 fluid ounces (fl oz)

Metric units for capacity:

1 liter (L)               = 1000 cubic centimeters (1000 cm3)

For further information in liter see page 521 of Basic Mathematics 9th Edition by Marvin L. Bittinger

A cubic centimeter is also known as a cc

1 milileterliter (L)    = 1 cubic centimeters (1 cm3) = 1 cc

Section 8.6 Time and Temperature

1 year (yr)             = 365 1/4 days

1 week (wk)           = 7 days

1 day                     = 24 hours (hr)

1 hour (hr)             = 60 minutes (min)

1 minute (min)       = 60 seconds (sec)

American temperature measurements are in Fahrenheit.  Metric temperature measurements are in Celsius.

Exact measurements of temperature; both American and Metric:

212°F (Fahrenheit) = 100°C (Celsius)

32°F (Fahrenheit)   = 0°C (Celsius)

To convert from Celsius to Fahrenheit temperatures use:

F = 1.8 ∙ C + 32

To convert from Fahrenheit to Celsius temperatures use:

C = (F – 32)/1.8

For further information in liter see page 528 of Basic Mathematics 9th Edition by Marvin L. Bittinger

 

Section 8.7 Converting Units of Area

American units of area

1 square foot (ft2)            = 144 square inches (in2)

1 square yard (yd2)          = 9 square foot (ft2)

1 acre                             = 43,560 square foot (ft2)

1 square mile (mi2)           = 640 acres

For further information in liter see pages 532 and 533 of Basic Mathematics 9th Edition by Marvin L. Bittinger

 

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