Statistics Flashcards
mean
ordinary average
heavily influenced by outliers (nb far away from the center of the list)
mean = sum of N entries / N N*mean = sum of entries
In a class, 18 students took a test and had an average of 70. Alicia and Burt then took the test and the average of all 20 students was 71. If Alicia got a 77, then what was Burt’s grade?
old sum = 1870 = 1260
new sum = 2071 = 1420
difference = 1420 - 1260 = 160
160 - 77 = 83
median
middle nb on an ordered list
or average of two middle nb
unaffected by outliers (nb far away from the center of the list)
List A = {10, 4, 7, 18}
List B = {x, 10, 4, 7, 18, 25}
If the median of List B is exactly 4 higher than the median of List A, what is the value of x?
median of List A = 8.5 median of List B = 12.5 Thre nb in B are below the median, so x must be above the median 12.5 = (10 + x) / 2 10 + x = 2*12.5 = 25 x = 15
mode
most frequent nb on a list
some lists have a single mode, some have more, and some have none (when all the nb are different from one another)
On a test in a class of more than 40 students, the scores had mean = median = mode = 81. Two absent students then took the test; they received grades of 83 and 47. What are the new mean & median? (A) mean = 81 and median = 81 (B) mean < 81 and median = 81 (C) mean = 81 and median < 81 (D) mean < 81 and median < 81
median doesn’t change (one over and one under)
A or B
47 is an outlier so mean is lower
B
In a certain company, 70% of employees are marketers who make an average of $40,000; 20% are programmers who make an average of $80,000; and 10% are managers, who make an average of $120,000. What is the average salary of all employees at this company?
0.740,000 + 0.280,000 + 0.1*120,000 = 56,000
average of whole
A1p1 + A2p2 + A3p3
At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $56,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
average closer to gold's than silver's salary S:G = 120:160 = 3:4 from As to Atotal is 4 parts from Atotal to Ag is 3 parts 7parts = $56,000 1part = $8,000 Atotal is $32,000 higher than As
range
max - min
standard deviation
deviation from the mean
list = {1, 4, 5, 7, 8}
mean = 5
deviations = {-4, -1, 0, 2, 3}
can only be positive or zero, never negative
SD = 0 only if all the nb on a list are identical to each other
if all the nb on a list are the same distance from the mean, that distance = SD
lots of pts close to the mean = small SD
lots of pts far from the mean = large SD
if we + or - K to/from every nb on a list, SD doesn’t change
if we multiply every nb on a list by positive nb K, SD also gets multiplied by K
On a certain test, the score had a mean = 300 and SD = 25. If John scored three SDs above the mean, what was John’s score?
John’s score = 300 + 3*25 = 375
Calculation of SD
start with a list of nb
calculate the mean
subtract the mean from every nb (list of deviations)
square every deviation (list of squared deviations)
find the average of the third list: the average squared deviation (variance)
take the square root of the variance (SD) in decimal form
A camp has 30 girls whose heights have an average of 130cm and an SD of 4cm. Suppose four more girls join the camp. Which set of heights for these four additional girls would most increase the SD of all the girls at the camp?
(A) {126, 126, 134, 134}
(B) {127, 129, 131, 133}
(C) {129, 130, 130, 131}
(D) {140, 140, 140, 140}C = decreases (closer to the mean than to the SD) B = decreases (deviations < SD) A = stays the same (deviations = SD) D = much larger deviations and SD
D
normal distribution
distribution = graph showing what values of a variable are more or less common in a population
normal distribution = bell curve
center of a ND = mean = median = mode
SD is used to measure distances from the mean
mean to SD = 2*34% = 68% (>2/3)
mean to 2SD = 95%
mean to 3SD = 99.7%
