Each year Money magazine publishes a list of "Best Places to Live in the United States." These listings are based on affordability, educational performance, convenience, safety, and livability. The below table shows the median household income of Money magazine’s top city in each U.S. state for (Money magazine website). Click on the datafile logo to reference the data. City Median Household Income ($) City Median Household Income ($) Pelham, AL 66,772 Bozeman, MT 49,303 Juneau, AK 84,101 Papillion, NE 79,131 Paradise Valley, AZ 138,192 Sparks, NV 54,230 Fayetteville, AR 40,835 Nashua, NH 66,872 Monterey Park, CA 57,419 North Arlington, NJ 73,885 Lone Tree, CO 116,761 Rio Rancho, NM 58,982 Manchester, CT 64,828 Valley Stream, NY 88,693 Hockessin, DE 115,124 Concord, NC 54,579 St. Augustine, FL 47,748 Dickinson, ND 71,866 Vinings, GA 73,103 Wooster, OH 43,054 Kapaa, HI 62,546 Mustang, OK 66,714 Meridian, ID 62,899 Beaverton, OR 58,785 Schaumburg, IL 73,824 Lower Merion, PA 117,438 Fishers, IN 87,043 Warwick, RI 63,414 Council Bluffs, IA 46,844 Mauldin, SC 57,480 Lenexa, KS 76,505 Rapid City, SD 47,788 Georgetown, KY 58,709 Franklin, TN 82,334 Bossier City, LA 47,051 Allen, TX 104,524 South Portland, ME 56,472 Orem, UT 54,515 Rockville, MD 100,158 Colchester, VT 69,181 Waltham, MA 75,106 Reston, VA 112,722 Farmington Hills, MI 71,154 Mercer Island, WA 128,484 Woodbury, MN 99,657 Morgantown, WV 38,060 Olive Branch, MS 62,958 New Berlin, WI 74,983 St. Peters, MO 57,728 Cheyenne, WY 56,593 a. Compute the mean and median for these household income data. Mean $ (to decimals) Median $ (to decimals) b. Compare the mean and median values for these data. What does this indicate about the distribution of household income data? The mean household income is - Select your answer -largerlessItem 3 than the median household income. This indicates that the distribution of household income is - Select your answer -positivelynegativelyItem 4 skewed. c. Compute the range and standard deviation for these household income data. Range $ (to the nearest whole number) Standard deviation $ (to decimals)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Each year Money magazine publishes a list of "Best Places to Live in the United States." These listings are based on affordability, educational performance, convenience, safety, and livability. The below table shows the
Click on the datafile logo to reference the data.
| City | Median Household Income ($) | City | Median Household Income ($) | |||
| Pelham, AL | 66,772 | Bozeman, MT | 49,303 | |||
| Juneau, AK | 84,101 | Papillion, NE | 79,131 | |||
| Paradise Valley, AZ | 138,192 | Sparks, NV | 54,230 | |||
| Fayetteville, AR | 40,835 | Nashua, NH | 66,872 | |||
| Monterey Park, CA | 57,419 | North Arlington, NJ | 73,885 | |||
| Lone Tree, CO | 116,761 | Rio Rancho, NM | 58,982 | |||
| Manchester, CT | 64,828 | Valley Stream, NY | 88,693 | |||
| Hockessin, DE | 115,124 | Concord, NC | 54,579 | |||
| St. Augustine, FL | 47,748 | Dickinson, ND | 71,866 | |||
| Vinings, GA | 73,103 | Wooster, OH | 43,054 | |||
| Kapaa, HI | 62,546 | Mustang, OK | 66,714 | |||
| Meridian, ID | 62,899 | Beaverton, OR | 58,785 | |||
| Schaumburg, IL | 73,824 | Lower Merion, PA | 117,438 | |||
| Fishers, IN | 87,043 | Warwick, RI | 63,414 | |||
| Council Bluffs, IA | 46,844 | Mauldin, SC | 57,480 | |||
| Lenexa, KS | 76,505 | Rapid City, SD | 47,788 | |||
| Georgetown, KY | 58,709 | Franklin, TN | 82,334 | |||
| Bossier City, LA | 47,051 | Allen, TX | 104,524 | |||
| South Portland, ME | 56,472 | Orem, UT | 54,515 | |||
| Rockville, MD | 100,158 | Colchester, VT | 69,181 | |||
| Waltham, MA | 75,106 | Reston, VA | 112,722 | |||
| Farmington Hills, MI | 71,154 | Mercer Island, WA | 128,484 | |||
| Woodbury, MN | 99,657 | Morgantown, WV | 38,060 | |||
| Olive Branch, MS | 62,958 | New Berlin, WI | 74,983 | |||
| St. Peters, MO | 57,728 | Cheyenne, WY | 56,593 |
a. Compute the
| Mean | $ (to decimals) |
| Median | $ (to decimals) |
b. Compare the mean and median values for these data. What does this indicate about the distribution of household income data?
The mean household income is - Select your answer -largerlessItem 3 than the median household income. This indicates that the distribution of household income is - Select your answer -positivelynegativelyItem 4 skewed.
c. Compute the
| Range | $ (to the nearest whole number) |
| Standard deviation | $ (to decimals) |
d. Compute the first and third
| First Quartile | $ (to decimals) |
| Third Quartile | $ (to decimals) |
e. How many values would be considered outliers are in these data? If an amount is zero, enter "0".
value(s) would be considered outlier(s).
What does this suggest about the data?
- Select your answer -Since there are outliers above the upper limit of the data, this is most likely why the mean is larger than the median.Since there are outliers below the lower limit of the data, this is most likely why the mean is smaller than the median.Since there are no outliers, this is most likely why the mean is approximately equal to the median.Item 10
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