2.1 Homework (modified r. bloom)

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

• a Find the sample mean $\overline{x}$
• b Find the sample standard deviation, $s$
• c Construct a histogram of the data.
• d Complete the columns of the chart.
• e Find the first quartile.
• f Find the median.
• g Find the third quartile.
• h Construct a box plot of the data.
• i What percent of the students saw fewer than three movies?
• j Find the 40th percentile.
• k Find the 90th percentile.

The median age for U.S. blacks currently is 30.1 years; for U.S. whites it is 36.6 years. (Source: U.S. Census)

• a Based upon this information, give two reasons why the black median age could be lower than the white median age.
• b Does the lower median age for blacks necessarily mean that blacks die younger than whites? Why or why not?
• c How might it be possible for blacks and whites to die at approximately the same age, but for the median age for whites to be higher?

Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows:

• a Find the sample mean $\overline{x}$
• b Find the sample standard deviation, $s$
• c Construct a histogram of the data.
• d Complete the columns of the chart.
• e Find the first quartile.
• f Find the median.
• g Find the third quartile.
• h Construct a box plot of the data.
• i What percent of the students owned at least five pairs?
• j Find the 40th percentile.
• k Find the 90th percentile.

600 adult Americans were asked by telephone poll, What do you think constitutes a middle-class income?The results are below. Also, include left endpoint, but not the right endpoint. ( Source: Time magazine; survey by Yankelovich Partners, Inc. )

• a What percent of the survey answered "not sure"?
• b What percent think that middle-class is from $25,000 - $50,000 ?
• c Construct a histogram of the data
  1. i Should all bars have the same width, based on the data? Why or why not?
  2. ii How should the<20,000 and the100,000+ intervals be handled? Why?
• d Find the 40th and 80th percentiles

Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year (Source: San Jose Mercury News).

• 177
• 205
• 210
• 210
• 232
• 205
• 185
• 185
• 178
• 210
• 206
• 212
• 184
• 174
• 185
• 242
• 188
• 212
• 215
• 247
• 241
• 223
• 220
• 260
• 245
• 259
• 278
• 270
• 280
• 295
• 275
• 285
• 290
• 272
• 273
• 280
• 285
• 286
• 200
• 215
• 185
• 230
• 250
• 241
• 190
• 260
• 250
• 302
• 265
• 290
• 276
• 228
• 265

• a Organize the data from smallest to largest value.
• b Find the median.
• c Find the first quartile.
• d Find the third quartile.
• e Construct a box plot of the data.
• f The middle 50% of the weights are from _______ to _______.
• g If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?
• h If our population were the San Francisco 49ers, would the above data be a sample of weights or the population of weights? Why?
• i Assume the population was the San Francisco 49ers. Find:
  • i the population mean, $\mu$ .
  • ii the population standard deviation, $\sigma$ .
  • iii the weight that is 2 standard deviations below the mean.
  • iv When Steve Young, quarterback, played football, he weighed 205 pounds. How many standard deviations above or below the mean was he?
• j That same year, the average weight for the Dallas Cowboys was 240.08 pounds with a standard deviation of 44.38 pounds. Emmit Smith weighed in at 209 pounds. With respect to his team, who was lighter, Smith or Young? How did you determine your answer?
• k Based on the shape of the data, what is the most appropriate measure of center for this data: mean, median, or mode? Explain.
• l Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your conclusion.
• m Are any data values further away than 2 standard deviations from the mean? Clearly state your conclusion and show numerical work to justify your answer.