SECTION 2.2 histogram,frequency, relative frequency , class width

1. 2.2.3 The​ class width is the difference between consecutive lower class limits.

class width .

11. 2.2.RA-7 Use the applet available .

moviendo the graph .

2. 2.2.9 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 (a) What was the most frequent outcome of the​ experiment? (b) What was the least​ frequent? (c) How many times did we observe an 8​? (d ) How many more 9​'s were observed than 11​'s? (e)Determine the percentage of time an 8 was observed. (f) Describe the shape of the distribution. .

(a) 5 (tallest) (b) 2 (smallest) (c) 12 (F of 8) (d) 9=11 - 11= 4 → 11-4= 7 (F of 9 - F of 11) (e) 12 = 12% (F of 8) (f) Skewed right .

12 2.2.49 (a) Why​ shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency​ distribution? .

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

9. 2.2.28-T (a) The accompanying table shows the median household income​ (in dollars) for 25 randomly selected regions. (b) Construct a frequency distribution. Use a first-class having a lower class limit of 35,000 and a class width of 5000. (c) Construct a frequency histogram (d) Describe the shape of the distribution. (e) Describe the shape of the distribution. (f) Repeat the process with 10,000

(a) Step 1 is to create Bin Column: Use Data/Bin Need Min & Class Width Step 2 is to create Class Column: Re-type Bin Column to make the real classes. Step 3 is to create Frequency Table: 1. Use Stat/Table/Frequency 2. Select 'Class' column 3. Select items under 'Statistics' 4. 'Compute (b) Graph/ Histogram/select column=/type= frequency compare graphs (d) The distribution is bell-shaped. ...

8 2.2.25-T 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. (a) Are these data discrete or​ continuous? (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? (e) What percentage of households in the survey have four or more​ televisions? (f) Construct a frequency histogram of the data. (g) Construct a relative frequency histogram of the data (h)Describe the shape of the distribution.

(a) The given data are discrete because they can only have whole number values. (b) statcrunch STAT/tables/frequency/select columns= var1/statistics= relative + F/Compute (c) sames as (b) (d) (e) check in RF (c) 3=0.2→ 0.2x100= 20% (f) 4 or more check in RF (c) total TV= F= 40 ≥ 4 → 2+1= 3 3 = 0.075 x 100 = 7.5% 40 (g) (h) Skewed to the right .

4. 2.2.RA-1 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. (b) Construct a relative frequency distribution of the data. (c) Using the results from part​ (b), what percentage of the stretches of highway have 3​ potholes? (d) Using the results from part​ (b), what percentage of the stretches of highway have 5 or more​ potholes? .

(a) statcrunch STAT/ Tables/ Frequency/Select columns:/statistics= Frequency or Relative F/COMPUTE (b) Already from ↑ (c) (look at pothole 3 =.143 ≈ 14.3% (d) total potholes = Frequency (a) = sum all 11+5+5+4+3+3+4 = 35 (look at potholes ≥ 5) 3+3+4 = 10 10 = 0.28 = 28.6% 35 .

6. 2.2.RA-3 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. (histogram=discrete= whole #) (b) Construct a relative frequency distribution with the first-class having a lower class limit of​ 30,000 and a class width of 6000. .

(a)Graph/ Histogram/select column=/type= frequency/ bins= start at= 30000/width= 5999/value above bar ✓/ compute show graph(you add to ..999 (b) same ↑ but with Relative frequency (edit in Graph) .

5. 2.2.15 o 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. (a) Construct a relative frequency distribution of the data. (b) What percentage of households has two children under the age of​ 5? (c) What percentage of households has one or two children under the age of​ 5? .

(a) # of Children Relative under 5 Frequency =% To find the frequency: statcrunch Graph/Bar plot/With summary/categories in= # of /counts in # households= (males)/ type= relative frequency/Order by= worksheet/display= value above bar/Compute Open big graph, click in each bar to see the relative F. #. (b) 34​% 9 look table ↑ 2 = .034x 100 = 34% (c) 64​% (sum al # households 1 table =50 1or 2 child = 15+17=32 32/50=0.64x100= 64% .

#13 EXAM 7. 2.2.23 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) Construct a relative frequency distribution. (continuos speed) (b) Choose the correct frequency histogram (c) Choose the correct relative frequency histogram (d) The percentage of players that had a top speed between 22 and 25.9 ​km/h was 12.73​%. ​ (e) The percentage of players that had a top speed less than 13.9 ​km/h was 0.5​%. .

(a) relative frequency distribution.(continuos) Graph/Bar plot/With summary/categories in= speed /counts in= (# players,males)/ type= relative frequency/Order by= worksheet/display= value above bar/Compute (b) and (c) are the same for Frequency and Relative F histogram graph (d) look at the (a) 22-25.9=0.1273= 12.73% (e) look at (a) 10-13.9 = 0.0050= 0.5% .

3. 2.2.11 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. Use the histogram (a) How many students were​ sampled? (b) Determine the class width. (c) Identify the classes and their frequencies. (d) Which class has the highest​ frequency? (e) Which class has the lowest​ frequency? (f) What percent of students had an IQ of at least 120​? (g) Did any students have an IQ of 168​?

(a)200 students ( sum all F top) (b) 10 (IQ scores van de 10 en 10) (c) 60-69, 1​; ​70-79, 3​; ​80-89, 13​; ​90-99, 41​; ​100-109, 53​; ​110-119, 43​; ​120-129, 33; ​130-139, 7​; ​140-149, 4​; ​150-159, 2 (one less ,NO from 60 to 70, just 60-69) (d) 100-009 (highest score or F= 53) (e) 60-69 (lowest F) (f) To find the​ %. 1. find the # students that have IQ scores at least 120. IQ scores ≥ to 120? 120-129, 130-139, 140-149, 150-159 33 + 7 + 4 + 2 = 46 (IQ ≥ 120) 46 = 0.23 = 23% 200 (g) the​ frequency, for any class greater than 160 is 0 (doesn't exist 168 IQ) ​◙ No, because there are no​ bars, or​ frequencies, greater than an IQ of 160.