Math 132 Up To Test 2

Front 1

What is a ratio?

Back 1

an (ordered) pair of numbers used to show a comparison between like and unlike qualities.

Written in the form "x to y", "x ÷ y" or "x:y" where y≠0

Front 2

What are the parts of a ratio?

Back 2

The numbers x and y are the terms of the ratio

Front 3

How do we determine if two ratios are equivalent?

Back 3

Two ratios are equivalent if their respective fractions are equivalent

Front 4

What is a proportion?

Back 4

For any two ratios a:b and c:d, a:b=c:d is a proportion

a:b=c:d if and only if ad=bc

Front 5

What is constant proportionality?

Back 5

If variables x and y are related by the equation y=kx then y is proportional to x and k is the constant of proportionality

y=kx is really saying that y:x=k

Front 6

What are the three main types of problems dealing with percentages?

Back 6

a)finding a percent of another number

b)finding a number when a percent of it is known

c) finding the percent that one number is of another

Front 7

How do we solve a problem asking to find the percent of a given number?

Back 7

Multiply the number by the percent as a decimal.

Front 8

How do we solve a problem asking to find the number when a percent of it is known?

Back 8

Divide the value of the given percent of the number by the percent as a decimal.

Ex. 240 is 40% of a number. Divide 240 by .40 to get 600 as the number.

Front 9

How do we solve a problem asking to find the percent that one number is of another?

Back 9

Divide the number that is the percentage of the other number by the other number and multiply by 100.

Front 10

What is the interest rate?

Back 10

The rate of return, expressed as a percent.

Front 11

What is the principle?

Back 11

The amount of money borrowed or invested

Front 12

What is compound interest?

Back 12

An investor earns money each year on the principle as well as on any interest previously earned.

Front 13

How is interest earned/paid calculated?

Back 13

By applying a compound interest to the principle.

Front 14

What is the formula for finding the final value of a principle with a given rate of compound interest?

Back 14

a=p(1+i/n)^nt

where p is the principle
i is the rate of annual interest as a decimal
n is the number of times interest is compounded per year
t is the number of years for the investment

Front 15

What is statistics?

Back 15

The science of collecting, classifying, and using data to interpret the significance ;of numerical information.

Front 16

What three things should data displays always have?

Back 16

1) a title explaining what the data represents

2) labels for the units or categories used in the display

3) scales that show the units and quanities of items displayed

Front 17

What are the features of a Frequency Table?

Back 17

various categories are listed in the table

tally marks are placed in each category to indicate the frequency with which observed data items fall into a given category

the relative frequence provieds the precent of the total number of data points represented by the frequency on each particular row of the table

Front 18

What are the features of a Dot or Line plot?

Back 18

easy to organize and view a set of data quickly

generally used with data sets of 40 numbers or less

scale goes horizontally. corresponding dots (or x's) are placed vertically upward of the scale

Front 19

What is the range of data?

Back 19

The difference between the smalles and the largest values in the data set.

Front 20

What are the features of a Stem and Leaf Plot?

Back 20

shows the actual data

is written in a vertical form, not horizontal

can have a dual leaf plotting (on either side of the stem) to compare two data sets

Front 21

How do we make a Stem and Leaf Plot?

Back 21

the tens/hundreds/thousands, etc. digits are the stem. the other digits are the leaves

if the leaves are more than one digit, separate with a comma

leaves are usually in ascending order

stem numbers are either ascending or descending

Front 22

What is a pictograph?

Back 22

A small icon or figure is used to represent the data values

each icon represents the same value

Front 23

What is a histogram?

Back 23

it has a horizontal and vertical axis. The horizontal has the values, from smallest to largest.
The vertical is the frequency

Solid rectangles are used to represent the frequencies

Front 24

What can we tell about a value from the height of it's corresponding rectangle, in a histogram?

Back 24

The height above an interval represents the frequency of the interval.

Front 25

What is a line graph?

Back 25

Line graphs are often used to show changes over a period of time. Dots are placed above the value on the horizontal axis at the frequency of that value (along the vertical axis), and the values are connected.

Front 26

How can we make a line graph from a histogram?

Back 26

Place a dot on the midpoint of the tops of the rectangles and connect them with line segments.

Front 27

What is a Bar Graph?

Back 27

a bar graph is used when the categories represent discrete groups, or at least non-adjacant intervals.

A line graph is similar to a histogram, but the rectangles are not touching.

Front 28

How is a bar graph more versatile than a histogram?

Back 28

We can have multiple bars for each category, to allow us to compare values for two different groups - ie. the heights of men vs women for different age groups.

Front 29

What is a pie chart?

Back 29

A pie chart is a circle, representing the whole, that is divided into pie-shaped sectors that represent the parts in proportion to the whole.

Front 30

How do we construct a pie chart?

Back 30

1. find the percentages that will be represented by each sector
2. multiply each percent by 360º to find the corresponding angle for each sector
3. draw a circle
4. draw a radius
5. draw a line segment at the corresponding angle for your first section
6. draw line segments at corresponding angles for each section
7. label the section, and make a title.

Front 31

What is a measure of central tendency?

Back 31

It is a numerical value used to describe the overal clustering of data

Front 32

What are the three measures of central tendency?

Back 32

Mean
Median
Mode

Front 33

What is mean?

Back 33

Mean is the average. It is the sum of the values in a set of data divided by the number of values in the set.

Denoted x bar

Front 34

What is median?

Back 34

The median of a set of data with an odd number of values is the middle value when the values are listed in increasing order.

The median of a set of data with an even number of valuse is the average of the two middle numbers when the values are listed in increasing order.

Denoted x hat

Front 35

What is mode?

Back 35

It is the value that occurs most often in a set of data

Front 36

What is range?

Back 36

The difference between the largest and smallest values in a set of data.

Front 37

What is the upper quartile?

Back 37

The median of the values greater than the median of the data

Front 38

What is the lower quartile?

Back 38

The median of the values less than the median of the data

Front 39

What is the interquartile range?

Back 39

The IQR is the difference between the upper and lower quartiles

Front 40

How do we find any outliers?

Back 40

Once the data is divided into quartiles and we know the IQR, we subtract 1.5 x IQR from the lower quartile, and add 1.5 x IQR to the upper quartile

any values that are beyond these two numbers are outliers

Front 41

How much data is in each quarter?

Back 41

Approximately 25%

Front 42

How much data is between the upper and lower quartiles?

Back 42

Approximately 50%

Front 43

What is a box and whisker plot?

Back 43

A graphical way to show the median, quartiles, and IQR of a set of data

Front 44

How do we make a box and whisker plot?

Back 44

After finding the median, and upper and lower quartiles, we make a vertical line for each, either above or below our horizontal axis.

Connect the lines with a horizontal line on the top and bottom (creating a box) This represents the IQR

Next, make a line above the lowest value, and one aboce the largest value. Draw a horizontal line from the box to these lines, creating the whiskers.

Front 45

What is a measure of variability?

Back 45

A number that describes the spread of dispertion of the data

Front 46

How do we calculate standard deviation?

Back 46

1. Fine the mean
2. Find the difference between each value and the mean
3. Square the differences
4. Determine the mean of the squared differences
5. Find the square root of this mean

Front 47

What can we say about the standard deviation, just by looking at a set of data?

Back 47

The more spread out the data, the greater the the standard deviation.

The less spread out the data, the smaller the standard deviation.

Front 48

How much of the data will lie within 2 standard deviations of the mean?

Back 48

At least 75%

Front 49

How many standard devations of the mean are needed until almost no values lie outside?

Back 49

3

Front 50

What is a sample?

Back 50

A collection of people or objects chosen to represent a larger collection of people or objects (the population)

Front 51

What is a random sample?

Back 51

A sample that is obtained such that every element in the population has the same chance of being selected for the sample.

Front 52

How can we generate a random sample?

Back 52

1. drawing from a hat

2. use a random number generator

3. use a random number table

Front 53

How do we denote the mean of a population?

Back 53

μ (mu)

we use a capital N for the total number of values in the population, instead of a small n

Front 54

How do we denote the standard deviation of a population?

Back 54

σ (lower case sigma)

Front 55

Why do we use a random sample?

Back 55

Sometimes a population is too large to find a mean and standard deviation of, so we find the mean and standard deviation of the random sample instead.

Front 56

What can we say about the mean and standard deviation of a large sample?

Back 56

The mean and standard deviation will be closer to the true value.

Front 57

How does a histogram approach a smooth curve?

Back 57

When the numbers of values in a set of data increase, the width of the intervals for the grouped data on the histogram becomes smaller

Front 58

what is a normal curve?

Back 58

a smooth bell-shaped curve

Front 59

What is normal distribution?

Back 59

The distribution of data in a normal curve.

Front 60

Are all normal curves the same shape?

Back 60

No, they vary according to to the mean and standard deviation.

Front 61

What can we say about the curve when we have a smaller standard deviation?

Back 61

The curve will be taller and thinner and the data will be less spread out.

Front 62

What can we say about the curve when we have a larger standard deviation?

Back 62

The curve will be lower and flatter and the data will be more spread out.

Front 63

What is the 68-95-99.7 rule?

Back 63

Given that the data is in a normal distribution:
within one standard deviation of the mean, we will find 68% of the data
within two standard deviations of the mean, we will find 95% of the data
within three standard deviations of the mean, we will find 99.7% of the data

Front 64

How can we describe relative percomance on a test?

Back 64

To give the percentage of people who did not score as high as a certain value.

Front 65

What is the pth percentile of a set of a data?

Back 65

A number that is greater than p% of the data and less than (100-p)% of the data

Front 66

What is the 50th percentile?

Back 66

The median of the data

Front 67

What is the 25th percentile?

Back 67

The lower quartile of the data

Front 68

What is the 75th percentile?

Back 68

The upper quartile of the data

Front 69

How do we find the p-th percentile of n values?

Back 69

1. arrange the values in increasing order
2. write p as a a decimal and calculate pn
3. if pn is not an integer, use the next highest integer for the pth percentile
4. if pn is an integer, use the mean of the values in position pn and pn+1 as the percentile

Front 70

What is a z-score?

Back 70

The z-score of a value x is the number of standard deviations that x is from the mean, in a normal distribution.

Front 71

How do we calculate a z-score?

Back 71

Z = (x-the mean)/s