Arithmetic reasoning Flashcards
Average
Standard deviation
Arithmetic mean
Take the sum of n numbers and divide by n
1
[Population] Standard deviation = sqrt (— sum(xi - xbar)^2)
N
1 Sample Standard deviation = sqrt(—— sum(xi - xbar)^2) (N-1)
1 mi = ? ft
1mi = 5,280 ft
Median of odd # of Data
The middle # if the data is listed in increasing order.
Median of an even # of data
Arithmetic mean (average) of the two middle numbers when the data is listed in increasing order.
Mode
Most frequently occurring # in the list. There may be more than one mode for a list of data
Range
Greatest # in the list - least #
Interquartile range
3rd quartile - 1st quartile To divide data into quartiles: 1) arrange in increasing order 2)find median M. M = Q2 3) divide data into 2 equal groups, find their median, it is Q1 and Q3
x + y = -1
Quantity A QuantityB
x y
One equation, 2 unknowns,
D) the relationship cannot be determined from the information given.
Can also plug in
x = 0
Then
y = 0
A certain store sells two types of pens: one type for $2 per pen and the other type for $3 per pen. If a customer can spend up to $25 to buy pens at the store and there is no sales tax, what is the greatest # of pens the customer can buy?
Start by looking at how many of the lesser value, $2, pens the customer can buy if the customer doesn’t buy any $3 pens.
25/2 = 12.5 .
So 12 pens for $2, 0 pens for $3.
Next consider $3 pens
11 $2 pens ($22) and 1 $3 pen = 12 pens total
10 $2 pens ($20) and 1 $3 pen = 11 pens total
9 $2 pens ($18) and 2 $3 pen= 11 pens total.
As the # of $2 pens decreases the total # of pens decreases.
Therefore max amount = 12 pens
A list of numbers has a mean of 8 and standard deviation of 2.5. If x is a # in the list that is 2 standard deviations above the mean, what is the value of x?
x = 2(2.5) + 8 x = 13
The following table shows the distribution of 200,000 physicians by specialty. Which of the following sectors represent more than 40,000 physicians?
A. Pediatrics - 21% B. Internal Medicine - 25% C. Surgery - 24% D. Anesthesiology - 3% E. Psychiatry - 6%
Find what percent of 200,000 is 40,000
40,000/200,000 = 0.2 = 20%
choices over 20% are A, B, C.
Profit
Profit, or gross profit = sales revenue - cost of production
If n is the integer, what is the sum of first two consecutive integers greater than n + 6?
(n+7)+(n+8)
In 2009 the property tax on each home in Town X was p percent of the assessed value of the home, where p is a constant. The property tax in 2009 on a home in Town X that had an assessed value of $125, 000 was $2, 500
Quantity A QuantityB
The property tax in 2009 on $3,000
a home in Town X that had
an assessed value of
$160, 000
$125,000p = $2,500 P = 125000/2500 P = 0.02 or 2%
2% of $160,000 is
160,000 * 0.02 = 3,200
3,200 > 3000
A>B
Congruent angles
Angles that have equal measures. Opposite angles
Acute angle
Less than 90 degrees
Obtuse angle
Angle b/w 90 and 180 degrees
Convex polygon
A polygon in which the measure of each interior angle is less than 180 degrees
Sum of interior angles of a polygon
(n-2)*180
Sum of hexagon (6-2)180=720
Regular polygon
A polygon in which all sides are congruent and all interior angles are congruent.
Quadrilateral
4 sided polygon
Equilateral triangle
Triangle with three congruent sides
Isosceles triangle
A triangle with at least two congruent sides
Congruent triangles
Two triangles that have the same shape and size