Common Core Math IUnit 1 Review Day

One-Variable Statistics

Warm-Up Job Number of people

having the jobAnnual Salary

President 1 200,000Vice President 1 50,000

Supervisor 2 25,000Sales Representative 4 21,000Warehouse Worker 2 15,000

Custodian 2 15,000Clerical Worker 3 12,000

1.Find the mean2.Find the median3.Identify any outliers4.Which is a better representation of the

center?

Homework Check 1.7

8. Describe the data in context. Why do you think the data is skewed?

The distribution of medals won at the 1984 Winter Olympics in Sarajevo, Yugoslavia, is skewed to the right with a median of 4 medals and an IQR of 7 medals. This means that the middle 50% of countries won between 2 and 8 medals. Two countries, East Germany and USSR, were outliers with 24 and 25 medals each, respectively. The data is skewed to the right because of the two high outliers. Typically at the Olympics, most countries win a small number of medals and a few countries win a large number of medals, making the distribution skewed to the right.

HW1.8

Write a few sentences comparing the two types of automobiles, based on the shape, center, spread, and any outliers of each data distribution.

The distribution of miles per gallon for cars is skewed t the right. Most cars have between 25 and 30 mpg in the city, with a few cars with as many as 40 mpg. The distribution of miles per gallon for SUVs is fairly symmetrical. In general, SUVs get fewer miles per gallon than cars. The mean for cars is 32.9 mpg in the city and for SUVs is only 16.6 mpg. There is more variability in miles per gallon for cars than for SUVs. Most SUVs are within 4 mpg of the average, whereas most cars are within 7 mpg of the average.

Data descriptionsShape: Symmetrical, Skewed left, skewed right, or

uniformOutliers: Use the 1.5IQR rule to identifyCenter: If data has outliers: use median

If data does not have outliers: use meanSpread: Address Standard Deviation, Range,

Interquartile Range

Measures of Center

Mean: add up all data values and divide the sum by the number of data values – use if no outliers!

Median: Put the numbers in order from least to greatest. Find the middle data. -- use if you have outliers

Number of data values:Odd: one valueEven: add the two center values and divide by 2

5 Number SummaryMin: lowest data value

Q1: Median of lower half

Median: Middle data value

Q3: Median of upper half

Max: highest data value

IQR

*the box in a boxplot*

IQR: Q3-Q1

Outliers

1. Calculate the IQR (Range of IQR “Q3-Q1”)2. Multiply the IQR by 1.5. 3. Add this number to Q3. 4. Any value above this amount is considered an

outlier. 5. Then subtract that number from Q1. 6. Any value below this amount is an outlier.

Measure of Spread

Range: Highest value – Lowest Value

Standard Deviation: USE YOUR CALCULATOR!!Stat, Edit (enter data values), Stat, over to calc, enter, 2nd 1 (for L1) Enter.

Be able to create

1. Frequency Table2. Dotplot3. Histogram 4. Boxplot

Homework: 2.8