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Why do we need to group data in the form of a frequency table? Explain briefly.

How are the relative frequencies and percentages of categories obtained from the frequencies of categories? Illustrate with the help of an example

Thirty adults were asked which of the following conveniences they would find most difficult to do without: television (T), refrigerator (R), air conditioning (A), public transportation (P), or microwave (M). Their responses are listed below. $$ \begin{array}{cccccccccc} \mathrm{R} & \mathrm{A} & \mathrm{R} & \mathrm{P} & \mathrm{P} & \mathrm{T} & \mathrm{R} & \mathrm{M} & \mathrm{P} & \mathrm{A} \\ \mathrm{A} & \mathrm{R} & \mathrm{R} & \mathrm{T} & \mathrm{P} & \mathrm{P} & \mathrm{T} & \mathrm{R} & \mathrm{A} & \mathrm{A} \\ \mathrm{R} & \mathrm{P} & \mathrm{A} & \mathrm{T} & \mathrm{R} & \mathrm{P} & \mathrm{R} & \mathrm{A} & \mathrm{P} & \mathrm{R} \end{array} $$ a. Prepare a frequency distribution table. b. Calculate the relative frequencies and percentages for all categories. c. What percentage of these adults named refrigerator or air conditioning as the convenience that they would find most difficult to do without? d. Draw a bar graph for the relative frequency distribution.

Briefly explain the three decisions that have to be made to group a data set in the form of a frequency distribution table.

How are the relative frequencies and percentages of classes obtained from the frequencies of classes? Illustrate with the help of an example.

Three methods-writing classes using limits, using the less-than method, and grouping data using single-valued classes-were discussed to group quantitative data into classes. Explain these three methods and give one example of each.

A sample of 80 adults was taken, and these adults were asked about the number of credit cards they possess. The following table gives the frequency distribution of their responses. $$ \begin{array}{lc} \hline \text { Number of Credit Cards } & \text { Number of Adults } \\ \hline 0 \text { to } 3 & 18 \\ 4 \text { to } 7 & 26 \\ 8 \text { to } 11 & 22 \\ 12 \text { to } 15 & 11 \\ 16 \text { to } 19 & 3 \\ \hline \end{array} $$ a. Find the class boundaries and class midpoints. b. Do all classes have the same width? If so, what is this width? c. Prepare the relative frequency and percentage distribution columns. d. What percentage of these adults possess 8 or more credit cards?

A data set on money spent on lottery tickets during the past year by 200 households has a lowest value of $$\$ 1$$ and a highest value of $$\$ 1167$$. Suppose we want to group these data into six classes of equal widths. a. Assuming that we take the lower limit of the first class as $$\$ 1$$ and the width of each class equal to $$\$ 200$$, write the class limits for all six classes. b. What are the class boundaries and class midpoints?

The accompanying table lists the 2006-07 median household incomes (rounded to the nearest dollar), for all 50 states and the District of Columbia. $$ \begin{array}{lccc} \hline \text { State } & \begin{array}{c} \text { 2006-07 Median } \\ \text { Household Income } \end{array} & \text { State } & \begin{array}{c} 2006-07 \text { Median } \\ \text { Household Income } \end{array} \\ \hline \text { AL } & 40,620 & \text { MT } & 42,963 \\ \text { AK } & 60,506 & \text { NE } & 49,342 \\ \text { AZ } & 47,598 & \text { NV } & 53,912 \\ \text { AR } & 39,452 & \text { NH } & 65,652 \\ \text { CA } & 56,311 & \text { NJ } & 65,249 \\ \text { CO } & 59,209 & \text { NM } & 42,760 \\ \text { CT } & 64,158 & \text { NY } & 49,267 \\ \text { DE } & 54,257 & \text { NC } & 42,219 \\ \text { D.C. } & 50,318 & \text { ND } & 44,708 \\ \text { FL } & 46,383 & \text { OH } & 48,151 \\ \text { GA } & 49,692 & \text { OK } & 41,578 \\ \text { HI } & 63,104 & \text { OR } & 49,331 \\ \text { ID } & 48,354 & \text { PA } & 49,145 \\ \text { IL } & 51,279 & \text { RI } & 54,735 \\ \text { IN } & 47,074 & \text { SC } & 42,477 \\ \text { IA } & 49,200 & \text { SD } & 46,567 \\ \text { KS } & 47,671 & \text { TN } & 41,521 \\ \text { KY } & 40,029 & \text { TX } & 45,294 \\ \text { LA } & 39,418 & \text { UT } & 54,853 \\ \text { ME } & 47,415 & \text { VT } & 50,423 \\ \text { MD } & 65,552 & \text { VA } & 58,950 \\ \text { MA } & 57,681 & \text { WA } & 57,178 \\ \text { MI } & 49,699 & \text { WV } & 40,800 \\ \text { MN } & 57,932 & \text { WI } & 52,218 \\ \text { MS } & 36,499 & \text { WY } & 48,560 \\ \text { MO } & 45,924 & & \\ \hline \end{array} $$ a. Construct a frequency distribution table. Use the following classes: \(36,000-40,999,41,000-\) \(45,999,46,000-50,999,51,000-55,999,56,000-60,999,61,000-65,999\) b. Calculate the relative frequencies and percentages for all classes. c. Based on the frequency distribution, can you say whether the data are symmetric or skewed? d. What percentage of these states had a median household income of less than \(\$ 56,000 ?\)

The following table gives the frequency distribution for the numbers of parking tickets received on the campus of a university during the past week for 200 students. $$ \begin{array}{cc} \hline \text { Number of Tickets } & \text { Number of Students } \\ \hline 0 & 59 \\ 1 & 44 \\ 2 & 37 \\ 3 & 32 \\ 4 & 28 \\ \hline \end{array} $$ Draw two bar graphs for these data, the first without truncating the frequency axis and the second by truncating the frequency axis. In the second case, mark the frequencies on the vertical axis starting with 25 . Briefly comment on the two bar graphs.