Section 2.2: Practice Homework

The ________ class limit is the smallest value within the class and the _________ class limit is the largest value within the class

Lower, upper

The following data represents the number of grams of fat in breakfast meals offered at a local fast food restaurant 1. Construct an ordered stem-and-leaf plot 2. The distribution is...

1. 0 - 3, 4, 5, 6, 8 1 - 0, 1, 3, 3, 3, 5, 6, 9 2 - 3, 3, 3, 4, 8 3 - 0, 3, 4 4 - 3 2. The distribution is skewed right

The data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. 1. Find the number of classes 2. The upper and lower class limits for the third class 3. The class width

1. 5 2a. 20 2b. 24.9 3. 5

The _______________ is the difference between consecutive lower class limits

Class Width

Determine whether the following statement is true or false The shape of the distribution shown is best classified as uniform

False - All the bars in a uniform distribution are approximately the same height while this graph has the highest frequency occurring in the middle and the frequencies tail off to the left and right of the middle in a symmetric way

Determine whether the following statement is true or false The shape of the distribution shown is best classified as skewed left

False - the given graph is skewed in the direction of the tail. Thus, the graph is classified as skewed right

Stem-and-leaf plots are particularly useful for large sets of data

False - they lose their usefulness when data sets are large or when they consist of a large range of values

The data in the accompanying table represents the ages of presidents of a country on their first days in office 1. Construct a stem-and-leaf plot 2. Describe the shape of the distribution

I would like to point out that no work had to be done, because all the other answers had something wrong with them and therefore could be eliminated, leaving only the one I give.... 1. President Ages 4 - 1 3 4 - 5 6 7 8 9 9 5 - 0 0 1 1 1 1 2 2 4 4 4 4 4 5 - 5 5 5 5 6 6 6 7 7 7 7 8 6 - 0 1 1 1 2 4 4 6 - 5 8 9 2. Bell shaped

For a number of people living in a household, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left or skewed right

Skewed right

Sometimes, data must be modified before a stem-and-leaf plot may be constructed. For example, the data in the accompanying table represent the five-year rate of return of 20 mutual funds and are reported to the hundredth decimal place. So, if we used the integer portion of the data as the stem and the decimals as the leaves, then the stems would be 8, 9, 10...., 19; but the leaves would be two digits (such as 94, 53, and so on). This is not acceptable since each leaf must be a single digit. To resolve this problem, we round the data to the nearest tenth. 1. Round the data to the nearest tenth 2. Draw a stem-and-leaf plot of the modified data 3. Describe the shape of the distribution

1. 14.17 = 14.2 15.88 = 15.9 15.16 = 15.2 12.21 = 12.2 13.08 = 13.1 14.48 = 14.5 13.88 = 13.9 13.26 = 13.3 12.16 = 12.2 14.02 = 14.0 15.82 = 15.8 14.59 = 14.6 15.59 = 15.6 14.65 = 14.7 13.36 = 13.4 15.44 = 15.4 13.47 = 13.5 15.24 = 15.2 15.72 = 15.7 12.55 = 12.6 2. 12 - 2, 2, 6 13 - 1, 3, 4, 5, 9 14 - 0, 2, 5, 6, 7 15 - 2, 2, 4, 6, 7, 8, 9 3. The distribution is skewed left because the left tail is longer than the right tail

To predict future enrollment in a school district, fifty households within the district were sampled, and asked to disclose the number of children under the age of five living in the household. The results of the survey are presented in the table 1. Construct a relative frequency distribution of the data 2. What percentage of households has two children under the age of 5? 3. What percentage of households has one or two children under the age of 5?

1. 0 = .26 1 = .34 2 = .3 3 = .06 4 = .04 2. 30% 3. 64%

The following frequency histogram represents the IQ scores of a random sample of seventh-grade students. IQs are measured to the nearest whole number. The frequency of each class is labeled above each rectangle. 1. How many students were sampled? 2. Determine the class width 3. Identify the classes and their frequencies 4. Which class has the highest frequency? 5. Which class has the lowest frequency? 6. What percentage of students had an IQ of at least 130? 7. Did any students have an IQ of 162?

1. 200 2. 10 3. 60-69, 2.... the only option that begins with this answer is the right choice 4. 100-109 5. 150-159 6. 7% 7. No, because there are no bars, or frequencies, greater than an IQ of 160

An experiment was conducted in which two fair dice were thrown 100 times. The sum of the pips showing on the dice was then recorded. The frequency histogram to the right gives the results. 1. What was the most frequent outcome of the experiment? 2. What was the least frequent? 3. How many times did we observe a 7? 4. How many more 6's were observed than 12's? 5. Determine the percentage of time a 7 was observed 6. Describe the shape of the distribution

1. 7 2. 12 3. 20 4. 14 5. 20% 6. Bell-shaped

THIS QUESTION IS LONG SO THE SECOND SET OF QUESTIONS IS ON THE NEXT CARD: The accompanying table shows the tax, in dollars, on a pack of cigarettes in 30 randomly selected cities: 1. Construct a frequency distribution. Use a first class having a lower class limit of 0 and a class width of .50 2. Construct a relative frequency distribution. Use a first class having a lower class limit of 0 and a class width of .50 3. Construct a frequency histogram 4. Construct a relative frequency histogram 5. Describe the shape of the distribution

1. Tax | Frequency 0 - .49 = 4 .50 - .99 = 9 1 - 1.49 = 4 1.5 - 1.99 = 5 2 - 2.49 = 3 2.5 - 2.99 =3 3 - 3.49 = 1 3.5 - 3.99 = 0 4 - 4.49 = 1 2. Tax | Relative Frequency 0 - .49 = .13 .50 - .99 = .3 1 - 1.49 = .13 1.5 - 1.99 = .17 2 - 2.49 = .1 2.5 - 2.99 = .1 3 - 3.49 = .03 3.5 - 3.99 = 0 4 - 4.49 = .03 3. C... it was literally the only graph that made sense for these numbers... if you get this wrong I can't really help you :c 4. C again... this one should also be obvious 5. The distribution is skewed-right

A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtains the data in the accompanying table 1. Are these data discrete or continuous? Explain. 2. Construct a frequency distribution of the data 3. Construct a relative frequency distribution of the data 4. What percentage of households in the survey have three televisions? 5. What percentage of households in the survey have four or more televisions? 6. Construct a frequency histogram of the data 7. Construct a relative frequency histogram 8. Describe the shape of the distribution. The distribution is _________________.

1. The given data are discrete because they can only have whole number values 2. 0 = 2 1 = 13 2 = 14 3 = 9 4 = 1 5 = 1 3. 0 = .05 1 = .325 2 = .35 3 = .225 4 = .025 5 = .025 4. 22.5% 5. 5% 6. C, should look like and upside down U, from tallest to shortest it should be 2, 1, 3, 0, 4 &5 7. D, literally it's the same exact graph as 6 but the numbers on the y-axis are different 8. Skewed right

Determine the original set of data 1 0 1 6 2 1 4 4 7 9 3 3 5 5 5 8 4 0 1 Legend 1 0 represents 10 There is normally a line between the numbers on the left and the set of numbers on the right but it looked jacked up when I put the line, so you'll just have to imagine it's there, sorry. The original set of data is...

10, 11, 16, 21, 24, 24, 27, 29, 33, 35, 35, 35, 37, 38, 40, 41

WELCOME TO PT 2 OF THIS SORCERY: The accompanying table shows the tax, in dollars, on a pack of cigarettes in 30 randomly selected cities 6. Construct a frequency distribution using a class width of 1 7. Construct a relative frequency distribution 8. Construct a frequency histogram 9. Construct a relative frequency histogram 10. Describe the shape of the distribution 11. Does one frequency distribution provide a better summary of the data than the other? Explain

6. Tax | Frequency 0 - .99 = 13 1 - 1.99 = 9 2 - 2.99 = 6 3 - 3.99 = 1 4 - 4.99 = 1 7. Tax | Relative Frequency 0 - .99 = .43 1 - 1.99 = .3 2 - 2.99 = .2 3 - 3.99 = .03 4 - 4.99 = .03 8. A.... it starts off high and then goes straight to 1 like my IQ doing stats for hours on end 9. C 10. The distribution is skewed-right 11. Both distributions have a similar shape, so either works well

___________ are the categories by which data are grouped

Classes