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Data on the number of times items appear in a store, the number of years since people last purchased a mattress, and the number of tv shows watched. It includes frequency distributions, stem-and-leaf plots, and exercises related to calculating various statistical measures such as quartiles, percentiles, and interquartile range. Topics in descriptive statistics, data visualization, and data analysis, which are commonly taught in introductory statistics courses at the university level. The information provided could be useful for students as study notes, lecture notes, or exercises to prepare for exams in statistics-related subjects.
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Exercise
The miles per gallon rating for 30 cars are shown below (lowest to highest). 19, 19, 19, 20, 21, 21, 25, 25, 25, 26, 26, 28, 29, 31, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 38, 38, 38, 41, 43, 43
Solution
Exercise
Solution
Exercise3.
Stem Stem Leaf 1 9 9 9 2 0 1 1 5 5 5 6 6 8 9 3 1 1 2 2 3 4 5 6 7 7 8 8 8 8 4 1 3 3
The height in feet of 25 trees is shown below (lowest to highest). 25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54
Stem Stem Leaf 2 5 7 3 3 4 4 4 5 7 7 8 9 9 9 4 0 1 5 6 7 9 5 0 0 3 3 4 4
T h e d a t a a r e t h
e prices of different laptops at an electronics store. Round each value to the nearest ten. Create a stem plot using the hundreds digits as the stems and the tens digits as the leaves. 249, 249, 260, 265, 265, 280, 299, 299, 309, 319, 325, 326, 350, 350, 350, 365, 369, 389, 409, 459, 489, 559, 569, 570, 610
Tabl e
Solution
Exercise
Solution
Exercise
Solution
Exercise
Several children were asked how many TV shows they watch each day. The results of the survey are shown in Table 1.. Number of TV Shows Frequency 0 12 1 18 2 36 3 7 4 2 Table 1.
The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. Table 1.40 shows the four seasons, the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct a bar graph showing the number of students. Seasons Number of students Proportion of population Spring 8 24% Summer 9 26% Autumn 11 32% Winter 6 18%
Solution
Exercise
Solution
Exercise
Using the data from Mrs. Ramirez’s math class supplied in Exercise 1.8 , construct a bar graph showing the percentages.
David County has six high schools. Each school sent students to participate in a county- wide science competition. Table 1.41 shows the percentage breakdown of competitors from each school, and the percentage of the entire student population of the county that goes to each school. Construct a bar graph that shows the population percentage of competitors from each school. High School Science competition population Overall student population Alabaster 28.9% 8.6% Concordia 7.6% 23.2% Genoa 12.1% 15.0% Mocksville 18.5% 14.3%
Exercise
Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars. Complete the table.
Data Value (# cars) Frequency Relative Frequency
Cumulative Relative Frequency
Solution
Exercise
Data Value (# cars) Frequency Relative Frequency Cumulative Relative Frequency 3 14 0.22 0. 4 19 0.29 0. 5 12 0.18 0. 6 9 0.14 0. 7 11 0.17 1.
What does the frequency column in Table 1.42 sum to? Why?
Solution 65
Exercise
What does the relative frequency column in Table 1.42 sum to? Why?
Solution 1
frequency tells the number of data points that have each value.
Exercise
What is the difference between cumulative relative frequency and relative frequency for each data value in Table 1.42?
Solution The relative frequency shows the proportion of data points that have each value. The cumulative relative frequency tells the proportion of data points that are equal to or less than each value.
Exercise
To construct the histogram for the data in Table 1.42 , determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram. Label the horizontal and vertical axes with words. Include numerical scaling.
Solution Answers will vary. One possible histogram is shown:
Exercise
Construct a frequency polygon for the following: a. Pulse Rates for Women Frequency 60 – 69 12 70 – 79 14 80 – 89 11 90 – 99 1 100 – 109 1 110 – 119 0 120 – 129 1
b.
Actual Speed in a 30 MPH Zone Frequency 42 – 45 25
Comment the updated figure titled, [a3]: AA: Replace this figure with "CNX_Stats_C02_M05a_023anno"
b. Find the midpoint for each class. These will be graphed on the x-axis. The frequency values will be graphed on the y-axis values
c. Find the midpoint for each class. These will be graphed on the x-axis. The frequency values will be graphed on the y-axis values.
Exercise
Construct a frequency polygon from the frequency distribution for the 50 highest ranked countries for depth of hunger. Depth of Hunger Frequency 230 – 259 21 260 – 289 13 290 – 319 5
Table 1.
Solution Find the midpoint for each class. These will be graphed on the x-axis. The frequency values will be graphed on the y-axis values.
Exercise
Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countries. Include an overlayed frequency polygon and discuss the shapes of the distributions, the center, the spread, and any outliers. What can we conclude about the life expectancy of women compared to men? Life Expectancy at Birth – Women Frequency 49 – 55 3 56 – 62 3 63 – 69 1 70 – 76 3
standard deviation of 11.93 years. For the men, we have an average life expectancy of 73.4 years with a standard deviation of 13.14 years. We can conclude that the women tend to live slightly longer than men in this sample.
Exercise
Construct a times series graph for (a) the number of male births, (b) the number of female births, and (c) the total number of births. Sex/ Year
Female 45,545 49,582 50,257 50,324 51,915 51,220 52, Male 47,804 52,239 53,158 53,694 54,628 54,409 54, Total 93,349 101,821 103,415 104,018 106,543 105,629 107,
Sex/ Year
Female 51,812 53,115 54,959 54,850 55,307 55,527 56,292 55, Male 55,257 56,226 57,374 58,220 58,360 58,517 59,222 58, Total 107, 9
Table 1. Sex/ Year
Female 56,099 56,431 57,472 56,099 57,472 58,233 60,109 60, Male 60,029 58,959 61,293 60,029 61,293 61,467 63,602 63,
Total 116, 8
Solution
Exercise
The following data sets list full time police per 100,000 citizens along with homicides per 100,000 citizens for the city of Detroit, Michigan during the period from 1961 to
Year 1961 1962 1963 1964 1965 1966 1967 Police 260.35 269.8 272.04 272.96 272.51 261.34 268. Homicides 8.6 8.9 8.52 8.89 13.07 14.57 21.
Year 1968 1969 1970 1971 1972 1973
