Unit 4.4 Interpreting Statistics

Percent means-

“Out of one hundred”

How would 77% be expressed as a fraction?

What is 77% in decimal form?

• 0.77

• 77 ÷ 100

What is the easiest way to solve a question like this: a student got 81/110 questions right on a test. What percentage did they get?

• 81 ÷ 110 × 100 = 74%

Define quartiles

• Three values that split a data set into four equal parts

• Q₁, Q₂, Q₃

• Most easily determined when data is arranged from low to high or high to low

• Once arranged, determine middle point which is the median and Q₂

• Q₁ splits the bottom half of the data

• Q₃ splits the top half of the data

• (3 splices gets you 4 parts!)

Describe quartiles with an odd number (easier one)

• The middle number will be the median (Q₂) with an equal number of values on either side

• Find the middle point of below and above the median and that’s Q₁ and Q₃

Describe quartiles with an even number (harder one)

• All Q’s will be partial whole numbers (e.g. 2.5)

If a question asked what would it mean if you scored in the highest quartile, how would you describe it?

• Above Q₃ value

• Top 25% of the data

Define percentile

A value which is obtained when an ordered data set is divided into 100 percentage parts

Define percentile rank

• Indicates the percentage of scores that are below the indicated score

• Ranked in the 100^th percentile? Means you are ranked 1^st because 100% of your competitors scored below you

• 82^nd score? Means 82% of the scores were below you

What is the formula for percentile? The answer found means what?

• Where x is the score you are determining the percentile ranking of

• If the answer is 67% this means you are ranked in the 67^th percentile

If someone scored in the 85^th percentile, does that mean their grade on the test was 85%?

• No

• Means 85% of the students obtained marks that were lower

• A value that indicates the student’s placement compared to all other students

When thinking about percentile, if a question states someone got a score of 92 and you need to determine how many people got the same score, do you include the person we’re investigating?

Yes

Are percentage and percentile the same?

• NO

• Percentage represents your individual result

• Percentile considers your result in comparison to the entire group of participants

Define statistical index

A single number calculated by combining several different quantities/prices/other measures

What is the plural form of index?

Indices

Why is the Consumer Price Index (CPI) important?

Because the rate at which it increases or decreases is a measure of inflation or deflation

What is the Consumer Price Index?

• Every month, StatsCan creates an imaginary basket of necessities and calculates how much it would cost in total

• Process is repeated monthly and the prices are compared

• Some prices in the basket may go up, some may go down

• The overall change in price is an indication of how the economy is doing

What is the Consumer Price Index based on? i.e. what do they compare it to?

• The reference/base year is 1992

• That year has been assigned the value of 100 and every year is compared to that one

What is the formula for the Consumer Price Index?

• Increase in CPI (top shelf) means you subtract the years from each other

What does it mean is the percentile is positive? Negative?

• Positive means there was a price increase between the years

• Negative means the price decreased over that time

If a question as you to determine the cost of something in a later year compared to an earlier year, what’s an easy way to do it?

• Take the number of the later year and divide it by the earlier year

• Multiply the answer by the known cost