MML 2.2
What is the shape of the distribution shown?
Skewed Right. (Notice that the distribution peaks from 6 to 9. The tail on the right side of this peak is longer than on the left side of the peak.)
Use the applet available below to complete parts (a) through (c).
(a) How many classes are in the histogram for the Five-Year Rate of Return data when the "Starting point" is 8 and the "Bin width" is 2? -6 classes (b) How many classes are in the histogram for the Five-Year Rate of Return data when the "Starting point" is 8 and the "Bin width" is 4? -3 classes (c) How many classes are in the histogram for the Five-Year Rate of Return data when the "Starting point" is 8 and the "Bin width" is 1? -12 classes
A researcher wanted to determine the number of televisions in households. He conducts a survey of 40 randomly selected households and obtained the data to the right. Draw a dot plot of the televisions per household.
Choose the correct dot plot below. -B
The data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league.
(a) The number of classes. -4 (b) The class limits for the second class. -Lower class limit is 16. -Upper class limit is 21.9. (c) The class width. -6 (16-10=6)
The ________ is the difference between consecutive lower class limits.
Class width.
________ are the categories by which data are grouped.
Classes
A group of 12 randomly selected students were asked how many traffic tickets they have received since they started driving.
Create a dot plot of the data. -D
The following data represent the number of potholes on 35 randomly selected 1-mile stretches of highway around a particular city.
(a) Construct a frequency distribution of the data. -Potholes; Frequency -1; 11 -2; 5 -3; 7 -4; 3 -5; 2 -6; 4 -7; 3 (b) Construct a relative frequency distribution of the data. -Potholes; Relative Frequency -1; 0.314 (11/35=0.314) -2; 0.143 (5/35=0.143) -3; 0.2 (7/35=0.2) -4; 0.086 (3/35=0.086) -5; 0.057 (2/35=0.057) -6; 0.114 (4/35=0.114) -7; 0.086 (3/35=0.086) (c) Using the results from part (b), what percentage of the stretches of highway have 3 potholes? -20% (0.2*100=20) (d) Using the results from part (b), what percentage of the stretches of highway have 5 or more potholes? -25.7% (0.057+0.114+0.086=0.257*100=25.7)
The data below represent the per capita (average) disposable income (income after taxes) for 25 randomly selected cities in a recent year.
(a) Construct a frequency distribution with the first class having a lower class limit of 30,000 and a class width of 6000. -Class; Frequency -30,000-35,999; 13 -36,000-41,999; 11 -42,000-47,999; 0 -48,000-53,999; 1 (b) Construct a relative frequency distribution with the first class having a lower class limit of 30,000 and a class width of 6000. --Class; Relative Frequency -30,000-35,999; 0.52 -36,000-41,999; 0.44 -42,000-47,999; 0 -48,000-53,999; 0.04
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.
(a) How many students were sampled? -200 (1+4+13+54+43+40+30+9+4+2=200) (b) Determine the class width. -10 (70-60=10) (c) Identify the classes and their frequencies. -60-69, 1; 70-79, 4; 80-89, 13; 90-99, 54; 100-109, 43; 110-119, 40; 120-129, 30; 130-139, 9; 140-149, 4; 150-159, 2. (d) Which class has the highest frequency? -90-99 (e) Which class has the lowest frequency? -60-69 (f) What percent of students had an IQ of at least 120? -22.5% (30+9+4+2=45/200=0.225*100=22.5) (g) Did any students have an IQ of 166? -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.
(a) What was the most frequent outcome of the experiment? -5 (b) What was the least frequent? -12 (c) How many times did we observe an 11? -5 (d) How many more 5's were observed than 7's? -4 (e) Determine the percentage of time an 11 was observed. -5% (5/100=0.05*100=5) (f) Describe the shape of the distribution. -Skewed right.
