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Santa Clara County, CA, has approximately $27,873$Japanese-Americans. Their ages are as follows:

a. Construct a histogram of the Japanese-American community in Santa Clara County, CA. The bars will not be the

same width for this example. Why not? What impact does this have on the reliability of the graph?

b. What percentage of the community is under age $35$?

c. Which box plot most resembles the information above?

Javier and Ercilia are supervisors at a shopping mall. Each was given the task of estimating the mean distance that shoppers live from the mall. They each randomly surveyed $100$shoppers. The samples yielded the following information.

a. How can you determine which survey was correct ?

b. Explain what the difference in the results of the surveys implies about the data.

c. If the two histograms depict the distribution of values for each supervisor, which one depicts Ercilia's sample? How do you know?

d. If the two box plots depict the distribution of values for each supervisor, which one depicts Ercilia’s sample? How do you know?

Use the following information to answer the next three exercises: We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.

Use the data from the David County science competition supplied in Exercise $2.10$. Construct a bar graph that shows the county-wide population percentage of students at each school.

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 $\stackrel{¯}{x}$.

b. Find the approximate sample standard deviation, s.

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$\stackrel{¯}{x}$.

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 ${40}^{th}$percentile.

k. Find the ${90}^{th}$percentile.

l. Construct a line graph of the data.

m. Construct a stemplot of the data.

Following are the published weights (in pounds) of all of the team members of the San Francisco $49ers$from a previous year.

role="math" localid="1648013012857" $$\begin{gathered} 177;205;210;210;232;205;185;185;178;210;206;212;184;174;185;242;188; \\ 212;215;247;241;223;220;260;245;259;278;270;280;295;275;285;290;272;273; \\ 280;285;286;200;215;185;230;250;241;190;260;250;302;265;290;276;228;265 \end{gathered}$$

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 included every team member who ever played for 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, $\mathrm{μ}$.

ii. the population standard deviation, $\mathrm{σ}$.

iii. the weight that is two 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 mean 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?

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of a representative sample of $12$of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The $12$ change scores are as follows:

$3;8;–1;2;0;5;–3;1;–1;6;5;–2$

a. What is the mean change score?

b. What is the standard deviation for this population?

c. What is the median change score?

d. Find the change score that is $2.2$ standard deviations below the mean.

Refer to$Figure2.50$determine which of the following are true and which are false. Explain your solution to each part in complete sentences.

a. The medians for all three graphs are the same.

b. We cannot determine if any of the means for the three graphs is different.

c. The standard deviation for graph b is larger than the standard deviation for graph a.

d. We cannot determine if any of the third quartiles for the three graphs is different.

In a recent issue of the IEEE Spectrum, 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference.

a. Organize the data in a chart.

b. Find the median, the first quartile, and the third quartile.

c. Find the 65th percentile.

d. Find the 10th percentile.

e. Construct a box plot of the data.

f. The middle 50% of the conferences last from _______ days to _______ days.

g. Calculate the sample mean of days of engineering conferences.

h. Calculate the sample standard deviation of days of engineering conferences.

i. Find the mode.

j. If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.

k. Give two reasons why you think that three to five days seem to be popular lengths of engineering conferences

A survey of enrollment at 35 community colleges across the United States yielded the following figures: 6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622

a. Organize the data into a chart with five intervals of equal width. Label the two columns "Enrollment" and "Frequency."

b. Construct a histogram of the data.

c. If you were to build a new community college, which piece of information would be more valuable: the mode or the mean?

d. Calculate the sample mean.

e. Calculate the sample standard deviation.

f. A school with an enrollment of 8000 would be how many standard deviations away from the mean?

Use the following information to answer the next two exercises. X = the number of days per week that 100 clients use a particular exercise facility.