2.36 Skew and surname frequencies: Researchers published a summary of the frequency of surnames based on U.S. Census data (Word et al., 2008). The table lists the frequencies of last names in the left column, the number of last names with that level of frequency in the next column, and then the cumulative number and cumulative percentage in the next two columns. For example, 2.3 million people have the last name Smith, the most common name in this data set. So, Smith would be one of the seven names listed in the top row—last names that occur more than 1,000,000 times in the population. In another example, more than 72,000 people have the last name Singh. So, Singh is one of the 3012 surnames in the third row—names that occur between 10,000 and 99,999 times in the population.

a. Is this a frequency table or a grouped frequency table? Explain your answer.

b. How is this table different from the tables you created in this chapter? Why do you think the researchers constructed this table differently?

c. Based on this table, does this distribution seem to be normal, negatively skewed, or positively skewed? Explain your answer.

d. Is there a floor effect or a ceiling effect? Explain your answer.

Last names Frequency of occurrence Number Cumulative number Cumulative percentage 1,000,000+ 7 7 0.0 100,000–999,999 268 275 0.0 10,000–99,999 3012 3287 0.1 1000–9999 20,369 23,656 0.4 100–999 128,015 151,671 2.4 50–99 105,609 257,280 4.1 25–49 166,059 423,339 6.8 10–24 331,518 754,857 12.1 5–9 395,600 1,150,457 18.4 2–4 1,056,992 2,207,449 35.3 1 4,040,966 6,248,415 100.0