2.2b Histograms and Frequency Tables with Technology - Calculator

Jennifer is a teacher who is reviewing the average scores on the 10 tests in her class last year. The average scores are shown below. Average Test Scores 82 81 79 79 78 80 77 78 80 76 Use a calculator to create a relative frequency distribution for the data. What is the relative frequency of an average test score of at least 80?

.4 The relative frequency of an average test score of 80 is 0.2, of 81 is 0.1, and of 82 is 0.1. Add these relative frequencies to find the relative frequency of an average test score of at least 80. 0.2+0.1+0.1=0.4

A high-end computer store is looking at the last 10 computer purchases made. The number of video cards in the computers sold is recorded in the table below. Video Cards Used 1 1 2 1 1 1 1 1 2 2 Use a calculator to create a relative frequency distribution for the data. What is the relative frequency of a computer purchased that had more than 1 video card?

0.3

A baseball manager records the number of home runs that his team hits in each of the last 10 games of the season. The results are shown in the table below. Home Runs Hit 2 0 0 4 1 0 3 2 1 1 Use a calculator to create a relative frequency distribution for the data. What is the relative frequency of a game with no home runs hit?

0.3 To create a relative frequency distribution using a graphing calculator (such as a TI-83, TI-83 Plus, or TI-84), follow these steps: 1. Press the STAT key. 2. Press the ENTER key to get to the data table screen. 3. Create a frequency distribution in the first three columns of the table with the data in the first column, the unique values in ascending order in the second column, and their frequencies in the third column. 4. Highlight the fourth column header L4 and press ENTER to edit the formula for this column. 5. From here, press the 2nd key and then 3, which tells the calculator to use the values in column L3. 6. Press the ÷ key. 7. Next, to use the sum function, press the 2nd key and then the STAT key to bring up the list menu. 8. Press the right arrow twice to move over to the MATH heading. 9. Under the MATH header the sum function is option 5, so press 5 and it will be added to the function. 10. Press the 2nd key and press 3 to have the calculator sum the values in column L3. 11. Press the ENTER key to complete the relative frequency distribution. The relative frequency of a game with no home runs will be the value in column L4 that is in the same row as the 0 in column L2. Thus, the relative frequency of a game with no home runs is 0.3.

A business randomly sends out a questionnaire to 10 of its customers asking for their feedback. The questionnaire asks the customers to rate the service from 1 to 5, with 1 being the worst and 5 being the best. Their responses are given below. What is the relative frequency of a customer that rated the service as 5? 5 5 4 3 4 5 4 5 5 3

0.5

A meteorologist predicts the high temperature for 10 consecutive days in a certain area as given in the table below. 73 73 76 70 81 75 74 76 68 73 Use a calculator to create a frequency distribution. In how many of the days is the predicted temperature not in the 70s?

2

The wait times in seconds for the last 10 transactions at a fast food restaurant are shown in the table. Wait Times 45 30 35 85 25 20 45 40 50 65 Use a calculator to create a histogram. How many of the wait times are at least 60 seconds?

2

A researcher selects 10 random people between the ages of 18 and 35 and asks them how many hours of sleep on average that they get each day. The researcher records the responses in the following table. 6.5 8 7 7 8.5 7.5 6 9 8 7.5 Use a calculator to create a frequency distribution. How many of the people average fewer than 8 hours of sleep?

6

A manufacturer takes random samples of products created at 10 different production facilities. The number of defective products produced at each facility is given in the table below. 5 7 4 4 3 6 5 5 7 6 Use a calculator to create a frequency distribution. How many of the production facilities had between 4 and 6, inclusive, defective items in the sample?

7

A video game developer doing internal research asks 10 randomly selected people who self-identify as "gamers" how many of the developer's games they have played. The responses the developer receives are given below. 0 2 1 1 0 1 0 2 1 1 Use a calculator to find a frequency distribution of the data. How many of the respondents have played at least one of the developer's games?

7 1. To create a frequency distribution using a calculator, first enter the data into column L1 of a list. Open the list by pressing the STAT key and then pressing ENTER. 2. Enter the data set into column L1. 3. Sort the data in column L1. To do this, press the 2nd key and then MODE. Make sure the resulting screen is clear. 4. Then, press the STAT key and then the 2 key to bring up the SortA( function. 5. Press the 2nd key and then the 1 key to insert list L1 into the SortA( function. Then press the ) key and ENTER to sort the data in list L1. The word "Done" should appear. 6. After this is complete, go back to the List screen by pressing STAT and then ENTER. 7. Next, in column L2, enter each unique data value from the data set once, in ascending order. In this case, enter 0, 1, and 2 into column L2. 8. Count the number of times that each of the values in column L2 occurs in the data set in L1. There are 3 people who answered 0, 5 people who answered 1, and 2 people who answered 2. 9. Enter these amounts in the corresponding rows in L3 to complete the frequency distribution. Notice that the number of respondents who have played at least one of the developer's games is what is needed. Since the possible responses in column L1 are 0, 1, and 2, the respondents who answered 1 and the respondents who answered 2 fit this criteria. Since 1 is the second entry in column L2, the number of respondents who answered 1 is the second entry in column L3, which is 5. Similarly, 2 is the third entry in column L2, so the number of respondents who answered 2 is the third entry in column L3, which is 2. Add the number of respondents who answered 1 to the number of respondents who answered 2 to get the total number of respondents who have played at least one of the developer's games. 5+2=7

A car magazine is comparing the top speed in miles per hour of 15 different sports cars. The speeds are included in the table below. Top Speeds 267.71 253 187 247.16 188 250.4 240.10 224 195 212 248.5 190 205 202 245 Use a calculator to create a histogram for the data. Use the default window size. What is the result?

Follow these steps to use a TI-83, TI-83 plus, or TI-84 calculator to create the histogram. 1. First, press the STAT key and then press ENTER. 2. Enter the data into column L1. 3. With all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu. 4. Press ENTER and make sure that Plot1 is set to On. 5. Use the directional keys to navigate to the Type selector. Move the selection to the third type in the top row and press ENTER. 6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1. 7. Lastly, press the ZOOM key and then press 9 in order to change the zoom to ZoomStat. When this is completed, the correct histogram will display on the calculator.

Jackie measures the heights in inches of 15 of her classmates. She writes the heights in the table below. Height in Inches 60 61 68 64 62 63 63 65 61 59 67 64 63 66 64 Use a calculator to create a histogram of the data. Use the default window size. What is the result?

Follow these steps to use a TI-83, TI-83 plus, or TI-84 calculator to create the histogram. 1. First, press the STAT key and then press ENTER. 2. Enter the data into column L1. 3. With all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu. 4. Press ENTER and make sure that Plot1 is set to On. 5. Use the directional keys to navigate to the Type selector. Move the selection to the third type in the top row and press ENTER. 6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1. 7. Lastly, press the ZOOM key and then press 9 in order to change the zoom to ZoomStat. When this is completed, the correct histogram will display on the calculator.

The number of calories in 10 popular fast food meals is given in the table below. Use a calculator to create a histogram of the data, and then interpret the plot. Set Xmin to 500, Xmax to 1000, and Xscl to 100. Calories 760 660 770 820 600 670 890 540 940 560

The histogram shows a right-skewed distribution, indicating that most meals are in the lower end of this range, with a few that have a higher number of calories. Follow these steps to use a TI-83, TI-83 plus, or TI-84 calculator to create the histogram. 1. First, press the STAT key and then press ENTER. 2. Enter the data into column L1. 3. With all of the data entered, press the 2nd key and then press the Y= key to open the STAT PLOT menu. 4. Press ENTER and make sure that Plot1 is set to On. 5. Use the directional keys to navigate to the Type selector. Move the selection to the third type in the top row and press ENTER. 6. Make sure that Xlist is set to L1 as this needs to be the same column as the list that the data were entered into previously. If it is not, highlight the value for Xlist and press 2nd and the 1 key for list L1. 7. Press the ZOOM key and then press the 9 key to change the zoom to ZoomStat. 8. Press the WINDOW key and change Xmin to 500, Xmax to 1000, and Xscl to 100 in order to fit the data and the intervals required. Then press GRAPH to return to the histogram. 9. Press the TRACE key and use the directional buttons to view the height of each bar. The histogram shows a longer right tail, so the distribution is right-skewed. It shows that most meals are in the lower end of this range, with a few that have a higher number of calories.

An information technology specialist is searching 10 databases for a certain keyword. The number of occurrences in each database is as follows: Occurrences 1 2 1 0 3 2 2 1 0 1 Create a relative frequency distribution using a calculator. What is the relative frequency of the databases where the keyword is found at least once?

To determine the relative frequency of databases where the keyword is found at least once, subtract the relative frequency of 0 occurrences, 0.2, from 1. 1−0.2=0.8 Therefore, the relative frequency of the keyword occurring at least once in a database is 0.8.