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2.56 A researcher from a search engine company runs Internet searches and times how long each one takes. She found that 17 searches took 0.01 to 0.05 seconds; 57 took 0.06 to 0.10 seconds; 134 took 0.11 to 0.15 sec- onds; 146 took 0.16 to 0.20 seconds; 398 took 0.21 to 0.25 seconds; 82 took 0.26 to 0.30 seconds; and 56 took 0.31 to 0.35 seconds. Graph the frequency distribution and comment on its shape.
A music teacher held an assembly at an elementary school during which he explained the different types of instruments to the children. Afterwards, he surveyed them as to what kind of instrument each would like to play. Here are the results: percussion 12, brass 3 42, and string 28. Graph the results and comment on the shape of the graph. 9, wind-
Graphs and shapes of distributions 2.53 A developmental psychologist observes how children interact with their parents and classifies the childrens attachment as secure, avoidant, resistant, or disorganized. He classifies 33 children as securely attached, 17 as avoidant, 13 as resistant, and 21 as disorganized. Graph this fre- quency distribution and comment on its shape. Attachment Styles of 84 Children b 25 20 15 10 Secure Disorganized Avoidant Resistant Attachment style Since the data are nominal, the order is arbitrary and discussing the shape of the distribution does not make sense.
2.52 For each scenario, tell what the real limits of the number/interval are: a. If a persons temperature is reported as 100.3 (and not 100.2 or 100.4), what is the interval within which the persons temperature re- b. If a family has 7 children, not 6 or 8, what is the interval within which c. If a persons IQ is reported as 115 (and not 114 or 116), what is the d. If nations populations are reported to the nearest million and the ally falls? the number of children they have really falls? interval within which the persons IQ really falls? United States has a population of 321 million, not 320 or 322, how many people really live in the United States? e. If a man has 3 televisions in his house, not 4 or 5, what is the interval within which the number of televisions he has really falls?
Real vs. apparent limits 2.51 Below are sets of consecutive numbers, or intervals, from frequency distributions for continuous variables. For the second number (or inter- val) in each set, the one in bold, identify the real lower limit, real upper limit, interval width, and midpoint. a. 27-30; 31-34; 35-38 b. 10-20; 30-10; 50-60 c. 2.00-2.49; 2.50-2.99; 3.00-3.49 d. 10; 11; 12 Real Lower Limit Real Upper Limit Interval Width Midpoint 30.50 25.00 2.495 10.50 34.50 45.00 2.995 11.50 4.00 20.00 500 1.00 32.50 35.00 2.745 11.00
2.50 For each variable, decide if it is continuous or discrete: a. The depth, in inches, a person can drive a 3-inch nail with one ham- b. The number of students in a classroom who are absent for at least ore c. The total number of days that students in a classroom are absent dur- d. How many friends one has on Facebook mer blow day during the month of February ing the month of February e. The amount of time, measured in seconds, that a person in a driving simulator keeps his or her eyes on the road while engaging in a cell phone conversation
2.49 For each variable, decide if it is discrete or continuous: a. The number of cases of flu diagnosed at a college in a given semester b. The weight, in grams, of a rats hypothalamus c. The number of teachers, including substitutes, in a school district who are certified to teach high school math d. The number of times that a rat pushes a lever in a Skinner box during a 15-minute period e. How long, in seconds, it takes applause to die dowa at the end of a school assembly (a) Discrete (b) Continuous (c) Discrete (d) Discrete (e) Continuous
Grouped Frequency Distribution for Number of Chairs in 41 College Class- rooms (Interval Width 20) Per- Number of IntervalFreCumulative cent Chairs Cumulative Percentage 100.00 9756 95.12 68.29 2683 Midpoint quencyFrequency 99.50 79.50 59.50 39.50 19.50 age 2.44 2.44 26.83 41.46 26.83 90-109 70-89 39 50-69 30-49 10-29 17 28 2.48 A professor of education was curious about students expectations of c success. She obtained a sample of college students at the start academi of their college careers and asked them what they thought their GPAs would be for the first semester. Below are the data she obtained. Make a grouped frequency distribution for the data, using an interval width of 0.5 and an apparent lower limit of 2.1 for the bottom interval. Report midpoint, frequency, cumulative frequency, percentage, and cumulative percentage 3.9,4.0,3.0,3.5,3.0,35,35,39,35,2.5,3.5,38,39,3.0,3.9,35, 3.9, 3.0, 3.5, 2.8,24, 2.7,2.6,3.4, 3.6, 2.5,3.8,2.9,26,2.4
2.47 A college registrar completes a survey of classrooms on campus in or- der to find out how many usable seats there are in each one. Make a grouped frequency distribution for her data, using an interval width of 20 and an apparent lower limit of 10 for the bottom interval. Report midpoint, frequency, cumulative frequency, percentage, and cumulative percentage. Here are the data the registrar collected: 12, 26, 18, 17, 102, 20, 35, 46, 50, 28, 29, 53, 75, 30, 37,45,58, 43, 42, 36, 50, 60, 55,45, 40, 23, 28, 38, 39, 40, 50, 60, 45, 36, 28, 40, 54, 62, 38, 58, and 24.
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Answer #1

2.56) Solution:-

Frequency distribution

Time(in sec.) Searches
0.01-0.05 17
0.06-0.10 57
0.11-0.15 134
0.16-0.20 146
0.21-0.25 398
0.26-0.30 82
0.31-0.35 56

500 398 400 300 200 146 134 100 82 57 56 17 0.01-0.05 0.08-0.10 0.11-0.15 0.18-0.20 0.21-0.25 0.26-0.30 0.31-0.35

From the above frequency distribution graph we can say shape is Left Skewed.

2.54) Solution:-

50 42 40 5 30 z 20 12 10 Percussion Wind String Instriments

From the above graph we can say that the shape of the graph is approximately Symmetric.

Here I have solved 2 questions, for the rest please repost the rest of the question. Comment if there is any doubt to understant at any point.

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