Section 2.2 HW

The​ _________________ is the difference between consecutive lower class limits.

class width

_________________ are the categories by which data are grouped.

classes

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

false

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. Complete parts​ (a) through​ (c) below. Number of Children < 5: 0, 1, 2, 3, 4 Number of Households: 16, 15, 13, 3, 3 ​(a) Construct a relative frequency distribution of the data. (b) What percentage of households has two children under the age of​ 5? _____________________ % (Type an integer or a decimal. Do not​ round.) ​(c) What percentage of households has one or two children under the age of​ 5? _______________ ​% (Type an integer or a decimal. Do not​ round.)

(a) 0 (0.32); 1 (0.3); 2 (0.26); 3 (0.06); 4 (0.06) (b) 26% (c) 56%

The data to the right represent the top speed​ (in kilometers per​ hour) of all the players​ (except goaltenders) in a certain soccer league. Find ​(a) the number of​ classes, ​(b) the class limits for the fourth ​class, and ​(c) the class width. Speed (km/hr): 10-15.9; 16-21.9; 22- 27.9; 28-33.9 Number of Players: 8, 22, 180, 422 ​(a) There are ___________________ classes. (Type a whole​ number.) ​(b) - The lower class limit for the fourth class is ____________________. ​(Type an integer or a decimal. Do not​ round.) - The upper class limit for the fourth class is _______________________. ​(Type an integer or a decimal. Do not​ round.) ​(c) The class width is _______________. ​(Type an integer or a decimal. Do not​ round.)

(a) 4 (b) 28, 33,9 (c) 6

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. Use the histogram to complete parts​ (a) through​ (f). ​(a) What was the most frequent outcome of the​ experiment? ​(b) What was the least​ frequent? ​(c) How many times did we observe a 9? (d) How many more 7​'s were observed than 10​'s? ​(e) Determine the percentage (%) of time a 9 was observed. ​(f) Describe the shape of the distribution. Choose the correct answer below. - uniform - bell-shaped - skewed left - skewed right

(a) 9 (b) 2 (c) 19 (d) 7 (e) 19% (f) skewed left

Discuss the advantages and disadvantages of histograms versus​ stem-and-leaf plots. A. Stem-and-leaf plots are more useful for large data sets and can display more information than histograms.​ However, they are more difficult to construct. B. Stem-and-leaf plots are easier to make and can contain more information than histograms.​ However, they are not very useful for large data sets. C. Stem-and-leaf plots provide a way to graphically compare​ data, unlike histograms.​ However, they are more difficult to construct. D. Stem-and-leaf plots can compare quantitative data to qualitative​ data, unlike histograms.​ However, they are not very useful for large data sets.

B. Stem-and-leaf plots are easier to make and can contain more information than histograms.​ However, they are not very useful for large data sets.

Violent crimes include​ murder, forcible​ rape, robbery, and aggravated assault. The data to the right represent the​ violent-crime rate​ (crimes per​ 100,000 population) by region of a certain country. Complete parts​ (a) through​ (f) below. Violent Crimes: Lower limit: 100 Upper Limit: 1400 Class Width: 100 ​(a) If thirteen classes are to be​ formed, choose an appropriate lower class limit for the first class and a class width. An appropriate lower class limit for the first class is ____________ with a class width of ​(b) Construct a frequency distribution. ​(c) Construct a relative frequency distribution. ​(d) Construct a frequency histogram of the data. Choose the correct histogram below. ​(e) Construct a relative frequency histogram of the data. Choose the correct histogram below. f) Describe the shape of the distribution. Choose the correct answer below. - The distribution is symmetric because the the left and right sides are approximately mirror images. - The distribution is skewed right because the right tail is longer than the left tail. - The distribution is skewed left because the right tail is longer than the left tail. - The distribution is symmetric because the bars in the histograms are all approximately the same height. - The distribution is skewed right because the left tail is longer than the right tail. - The distribution is skewed left because the left tail is longer than the right tail.

(a) 100, 100 (b) 100 (5), 200 (14), 300 (11), 400 (10), 500 (2), 600 (8), 700 (0), 800 (0), 900 (0), 1000 (0), 1100 (0), 1200 (0), 1300 (1) (c) 0.098, 0.294, 0.157, 0.216, 0.059, 0.157, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.020 (d) B (e) A (f) The distribution is skewed right because the right tail is longer than the left tail.

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. Complete parts​ (a) through​ (h) below. TV (40) ​(a) Are these data discrete or​ continuous? Explain. - The given data are discrete because they can take on any real value. - The given data are continuous because they can only have whole number values. - The given data are continuous because they can take on any real value. - The given data are discrete because they can only have whole number values. ​(b) Construct a frequency distribution of the data. ​(c) Construct a relative frequency distribution of the data. (d) What percentage of households in the survey have three​ televisions? __________________ ​% ​(Type an integer or a decimal. Do not​ round.) (e) What percentage of households in the survey have four or more​ televisions? ___________________​% ​(Type an integer or a decimal. Do not​ round.) (f) Construct a frequency histogram of the data. Choose the correct graph below. ​(g) Construct a relative frequency histogram of the data. Choose the correct graph below. (h) Describe the shape of the distribution. The distribution is _________________.

(a) The given data are discrete because they can only have whole number values. (b) 0 (2), 1 (15), 2 (12), 3 (8), 4 (2), 5 (1) (c) 0 (0.05), 1 (0.375), 2 (0.3), 3 (0.2), 4 (0.05), 5 (0.025) (d) 20% (e) 7.5% (f) Skewed Right graph (g) Skewed Right Graph (h) skewed right

An Internet media and market research firm measured the amount of time an individual spends viewing a specific Webpage. The data in the accompanying table represent the amount of​ time, in​ seconds, a random sample of 40 surfers spent viewing a Webpage. Create the graphical summary. Write a sentence that describes the data. (a) Create the graphical summary. Choose the correct graph below. (b) Write a sentence that describes the data. Choose the correct answer below. - The distribution is skewed right. - The distribution is skewed left. - The distribution is bell shaped. - The distribution is uniform.

(a) graph B (skewed right) (b) - The distribution is skewed right.

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

- 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.

For scores on a standardized exam, such as the SAT, in a country, ​, state whether you would expect a histogram of the data to be​ bell-shaped, uniform, skewed​ left, or skewed right. - skewed left - uniform - bell shaped - skewed right

- bell shaped

Determine whether the following statement is true or false. ​Stem-and-leaf plots are particularly useful for large sets of data. - false - true

- false - Stem-and- leaf plots lose their usefulness when data sets are large or when they consist of a large range of values.

Determine the original set of data. 1 | 0 1 5 2 | 1 4 4 7 9 3 | 3 5 5 5 7 9 4 | 0 1 ​Legend: 1 | 0 represents 10 The original set of data is _______________________

10, 11, 15, 21, 24, 24, 27, 29, 33, 35, 35, 35, 37, 39, 40, 41

Why​ shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency​ distribution? A. Classes​ shouldn't overlap so that they are open ended. B. Classes​ shouldn't overlap so that the class width is as small as possible. C. Classes​ shouldn't overlap so that the distribution is not skewed in one direction. D. Classes​ shouldn't overlap so there is no confusion as to which class an observation belongs.

D. Classes​ shouldn't overlap so there is no confusion as to which class an observation belongs.

Is the statement below true or​ false? There is not one particular frequency distribution that is​ correct, but there are frequency distributions that are less desirable than others. A. The statement is false. All correctly constructed frequency distributions for a given data set are valid and give the same information. B. The statement is false. There is only one correct frequency distribution for any given data set. C. The statement is true. Any correctly constructed frequency distribution is valid.​ However, some are less desirable because they take up more space. D. The statement is true. Any correctly constructed frequency distribution is valid.​ However, some choices for the categories or classes give more information about the shape of the distribution.

D. The statement is true. Any correctly constructed frequency distribution is valid.​ However, some choices for the categories or classes give more information about the shape of the distribution.

Select the correct choices that complete the sentence below. The​ ______ class limit is the smallest value within the class and the​ ______ class limit is the largest value within the class.

lower; upper