Statistics

Question 1

Signals for arithmetic mean?

Answer 1

1. Usually explicitly stated
2. Or is phrased as some amount per individual unit
   … “per capita income”
   …. “If equally shared, the cost per employee is $530”

Question 2

When you see a question talking about arithmetic averages and means, what is step 1?

Answer 2

Immediately Write down the formula

average = sum / number of terms

Question 3

When the average of a set is known to you, what should you do with that value? (It could be stated in Q stem)

Answer 3

Algebraically alter the original formula by writing it as…
Average * # of terms = Sum

Question 4

When you are given 2 averages…

Answer 4

write them down in a simple chart to keep track of the relations

Question 5

If you are trying to figure out a single value that was added between an original and now a new set…

Answer 5

1. Use the variant average formula for both sets
   - N * Average = Original sum
   - N-1 * New average = New sum
2. Take the difference between the sums and boom you have the missing value

Question 6

Solve: James earned a 2k commission, raising his average commission by $100. If his new average commission is $900, how many sales has he made?

Answer 6

1. Can be solved with as system of equations to find “# of terms”
2. Set up a chart

Old: 800 * N

New sale: 2000

New: 900 * N + 1

3. set old + sale = New
4. Remember question is asking N + 1, now how many sales originally did he have before the 2k commission

OR this formula

(commission - original average) / # of sales = increase in average

Question 7

Median depends on how many values for even sets…

Answer 7

The 2 middle values, the average is taken of the,

Question 8

When introducing unknown values to median problems consider…

Answer 8

if it was larger or smaller, how could it change the median. Maybe it would duplicate a value or be an extreme outlier

Question 9

When standard deviation equals zero…

Answer 9

all numbers in the set are duplicates, meaning there is ZERO spread

Question 10

When given mean and/or standard deviation of a set; what information is still unknown…

Answer 10

How many numbers are actually inside the set and what they all are

Question 11

There are 2 main types of standard deviation Q’s, what are they…

Answer 11

1. Changes in standard deviation when set is transformed
2. Comparisons of standard deviations between multiple sets

Question 12

If a set is increased by a factor of 7; what happens to standard deviation…

Answer 12

the original standard deviation is multiplied by 7