Standard Deviation Investigation
Distribution Investigation Name _____________________________
Use the data below for the activity. (Unemployment Rates by State, 2009)
|State |Rate |State |Rate |State |Rate |
|NORTH DAKOTA |3.6 |ALASKA |7.9 |DISTRICT OF COLUMBIA |10.0 |
|SOUTH DAKOTA |4.5 |WISCONSIN |7.9 |GEORGIA |10.0 |
|NEBRASKA |4.8 |COLORADO |8.0 |KENTUCKY |10.0 |
|NEW HAMPSHIRE |5.9 |MAINE |8.0 |NORTH CAROLINA |10.0 |
|VERMONT |6.0 |NEW MEXICO |8.2 |INDIANA |10.1 |
|HAWAII |6.3 |NEW YORK |8.2 |TENNESSEE |10.1 |
|KANSAS |6.5 |TEXAS |8.2 |ALABAMA |10.3 |
|IOWA |6.8 |DELAWARE |8.5 |ILLINOIS |10.4 |
|MINNESOTA |6.8 |WEST VIRGINIA |8.5 |OHIO |10.5 |
|OKLAHOMA |6.8 |CONNECTICUT |8.8 |OREGON |10.5 |
|WYOMING |6.8 |IDAHO |8.8 |SOUTH CAROLINA |10.7 |
|LOUISIANA |7.0 |WASHINGTON |8.9 |MISSISSIPPI |11.0 |
|VIRGINIA |7.0 |MASSACHUSETTS |9.0 |FLORIDA |11.4 |
|MARYLAND |7.1 |MISSOURI |9.1 |RHODE ISLAND |12.0 |
|UTAH |7.2 |PENNSYLVANIA |9.2 |CALIFORNIA |12.3 |
|MONTANA |7.3 |ARIZONA |9.6 |MICHIGAN |13.2 |
|ARKANSAS |7.5 |NEW JERSEY |9.6 | | |
1) Create a histogram to represent the distribution of the 2009 unemployment rates. Calculate the numerical summary for this data and describe the distribution.
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2) One way to estimate a percentile is by finding the data values rank. For example if a state was ranked 45th out of 50 (of values written from lowest to highest), that state would be at the 90th percentile (45 ÷ 50 = 0.9 = 90% )
At what estimated percentile is Georgia? Would this percentile represent a good result? Explain.
3) What state is at the 30th percentile? (Hint: find the ranking at 30% of the 50 states)
4) Calculate the z-score for Georgia and the state at the 30th percentile.
5) What would be the unemployment rate for a state that has a z-score of -1.29? Round to the nearest tenth. Which state would this represent?
6) What would be the unemployment rate for a state that has a z-score of 0.87? Round to the nearest tenth. Which state would this represent?
7) Use the calculated mean and standard deviation to complete the values that should appear at each mark on the number line below.
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8) Count the number of data values that fall between each value on the number line above. Represent this as a dotplot on the number line above. See sample below.
1.3 1.8 2.3
|---------|---------| This shows that 4 states had unemployment rates that fell between 1.3 and 1.8.
9)
a) What percent of the data falls within 1 standard deviation of the mean?
b) What percent of the data falls within 2 standard deviations of the mean?
c) What percent of the data falls within 3 standard deviations of the mean?
10) Draw a smooth curve over the top of each column of dots. This is called a density curve.
11) Describe the distribution of unemployment rates for the 50 states.
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