Stat 2.1 HW
Heights of adult males are known to have a normal distribution. A researcher claims to have randomly selected adult males and measured their heights with the resulting relative frequency distribution as shown here. Identify two major flaws with these results. Height (cm) 130-144 145-159 160-174 175-189 190-204 Relative Frequency 24% 26% 21% 27% 29%
- The sum of the relative frequencies is 127%, but it should be 100%, with a small possible round-off error. - All of the relative frequencies appear to be roughly the same. If they are from a normal distribution, they should start low, reach a maximum, and then decrease.
Identify the lower class limits (in 1000 cells/μL). Blood Platelet Count of Males (1000 cells/μL) 0-99 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 2 53 81 14 0 0 1
0, 100, 200, 300, 400, 500, 600
Identify the class boundaries (in 1000 cells/μL). Blood Platelet Count of Males (1000 cells/μL) 0-99 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 2 53 81 14 0 0 1
0, 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5
The following data show the ages of recent award-winning male actors at the time when they won their award. Make a frequency table for the data, using bins of 20-29, 30-39, and so on. 39, 34, 41, 31, 56, 44, 49, 67, 20, 53, 35, 42, 73, 49, 40, 34, 41, 35, 49, 58, 42, 31, 47, 62, 36, 36, 58, 49, 44, 70, 47, 54, 33, 37 No. of actors 20-29 30-39 40-49 50-59 60-69 70-79
1 11 13 5 2 2
Identify the class width. Blood Platelet Count of Males (1000 cells/μL) 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 26 92 27 1 4
100
Identify the class width (in 1000 cells/μL). Blood Platelet Count of Males (1000 cells/μL) 0-99 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 2 53 81 14 0 0 1
100
Identify the lower class limits. Blood Platelet Count of Males (1000 cells/μL) 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 26 92 27 1 4
100, 200, 300, 400, 500
Identify the class midpoints. Blood Platelet Count of Males (1000 cells/μL) 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 26 92 27 1 4
149.5, 249.5, 349.5, 449.5, 549.5
Identify the number of individuals included in the summary. Blood Platelet Count of Males (1000 cells/μL) 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 26 92 27 1 4
150
Identify the number of individuals included in the summary. Blood Platelet Count of Males (1000 cells/μL) 0-99 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 2 53 81 14 0 0 1
151
Identify the upper class limits. Blood Platelet Count of Males (1000 cells/μL) 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 26 92 27 1 4
199, 299, 399, 499, 599
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. 0.37, 0, 0, 0, 0.21, 0, 0.15, 0, 0.01, 0.07, 0.57, 0, 0, 0.18, 0, 0.26, 0, 0.42, 0, 1.33, 0, 0, 0.16, 0, 0.02, 0, 0.27, 0, 0.11, 0 Daily Rainfall (in inches) 0.00-0.19 0.20-0.39 0.40-0.59 0.60-0.79 0.80-0.99 1.00-1.19 Find the frequency.
23 4 2 0 0 0 1
The data represents the body mass index (BMI) values for 20 females. Construct a frequency distribution beginning with a lower class limit of 15.0 and use a class width of 6.0. 17.7, 27.7, 19.2, 27.8, 33.5, 23.8, 21.6, 44.9, 26.3, 18.3, 24.6, 31.2, 22.9, 28.5, 37.7, 26.6, 23.3, 21.6, 39.1, 24.7 BMI 15.0-20.9 21.0-26.9 27.0-32.9 33.0-38.9 39.0-44.9
3 9 4 2 2
Identify the class midpoints (in 1000 cells/μL). Blood Platelet Count of Males (1000 cells/μL) 0-99 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 2 53 81 14 0 0 1
49.5, 149.5, 249.5, 349.5, 449.5, 549.5, 649.5
Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Time (sec) 60-119 120-179 180-239 240-299 300-359 Frequency 9 23 14 2 5
53
Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weights are listed below. Construct a frequency distribution with 10 classes. 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 8, 8, 9, 9 Last Digit 0 1 2 3 4 5 6 7 8 9
8 2 1 3 1 10 2 0 2 2
A frequency table of grades has five classes (A, B, C, D, F) with frequencies of 4, 15, 18, 5, and 3 respectively. Using percentages, what are the relative frequencies of the five classes? A: 4 B: 15 C: 18 D: 5 F: 3
8.89% 33.33% 40% 11.11% 6.67%
Identify the upper class limits (in 1000 cells/μL). Blood Platelet Count of Males (1000 cells/μL) 0-99 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 2 53 81 14 0 0 1
99, 199, 299, 399, 499, 599, 699
Identify the class boundaries. Blood Platelet Count of Males (1000 cells/μL) 100-199 200-299 300-399 400-499 500-599 600-699 Frequency 26 92 27 1 4
99.5, 199.5, 299.5, 399.5, 499.5, 599.5
Construct the cumulative frequency distribution for the given data. Age (years) of Best Actress when award was won v frequency 20-29L: 25 30-39: 36 40-49: 12 50-59: 2 60-69: 6 70-79: 1 80-89: 1
Age (years) of Best Actress when award was won v Cumulative Frequency Less than 30: 25 Less than 40: 61 Less than 50: 73 Less than 60: 75 Less than 70: 81 Less than 80: 82 Less than 90: 83
Among fatal plane crashes that occurred during the past 55 years, 563 were due to pilot error, 52 were due to other human error, 322 were due to weather, 79 were due to mechanical problems, and 428 were due to sabotage. Construct the relative frequency distribution.
Cause v Relative Frequency Pilot error: 39% Other human error: 3.6% Weather: 22.3% Mechanical problems: 5.5% Sabotage: 29.6%
Construct the cumulative frequency distribution for the given data. Daily Low (°F) v Frequency 35-39: 2 40-44: 4 45-49: 6 50-54: 9 55-59: 5 60-64: 5 65-69: 1
Daily Low Temperature (°F) v Cumulative Frequency Less than 40: 2 Less than 45: 6 Less than 50: 12 Less than 55: 21 Less than 60: 26 Less than 65: 31 Less than 70: 32
Use the given categorical data to construct the relative frequency distribution. Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 52, 66, 68, 55, 63, 44, 52.
Day v Relative Frequency Monday: 13% Tuesday: 16.5% Wednesday: 17% Thursday: 13.75% Friday: 15.75% Saturday: 11% Sunday: 13%
A _______ helps us understand the nature of the distribution of a data set.
Frequency Distribution
Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria? Temperature (°F) 35-39 40-44 45-49 50-54 55-59 60-64 65-69 Frequency 3 0 6 14 7 5 1
No, the distribution does not appear to be normal
Does the frequency distribution appear to be roughly a normal distribution? The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.00 and use a class width of 0.20. 0.37, 0, 0, 0, 0.21, 0, 0.15, 0, 0.01, 0.07, 0.57, 0, 0, 0.18, 0, 0.26, 0, 0.42, 0, 1.33, 0, 0, 0.16, 0, 0.02, 0, 0.27, 0, 0.11, 0 Daily Rainfall (in inches) 0.00-0.19 0.20-0.39 0.40-0.59 0.60-0.79 0.80-0.99 1.00-1.19
No, the distribution is not symmetric and the frequencies do not start off low.
Is it possible to identify the exact values of all of the original service times? Time (sec) 60-119 120-179 180-239 240-299 300-359 Frequency 9 23 14 2 5
No. The data values in each class could take on any value between the class limits, inclusive.
_______ are sample values that lie very far away from the majority of the other sample values.
Outliers
Among fatal plane crashes that occurred during the past 55 years, 563 were due to pilot error, 52 were due to other human error, 322 were due to weather, 79 were due to mechanical problems, and 428 were due to sabotage. What is the most serious threat to aviation safety, and can anything be done about it?
Pilot error is the most serious threat to aviation safety. Pilots could be better trained.
Construct one table that includes relative frequencies based on the frequency distributions shown below, then compare the amounts of tar in nonfiltered and filtered cigarettes. Tar (mg) in Nonfiltered Cigarettes 18-23: 2 24-29: 2 30-35: 13 36-41: 7 42-47: 1 Tar (mg) in Filtered Cigarettes 6-11: 1 12-17: 2 18-23: 7 24-29: 15
Relative Frequency (Nonfiltered) vs Relative Frequency (Filtered) (percentages) 6−11: 0 v 4 12−17: 0 v 8 18−23: 8 v 28 24−29: 8 v 60 30−35: 52 v 0 36−41: 28 v 0 42−47: 4 v 0
In a _______ distribution, the frequency of a class is replaced with a proportion or percent.
Relative frequency
Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weights are listed below. 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 8, 8, 9, 9 Based on the distribution, do the weights appear to be reported or actually measured?
The weights appear to be reported because there are disproportionately more 0s and 5s.
Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of those weights are listed below. 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 8, 8, 9, 9 What can be said about the accuracy of the results?
They are likely not very accurate because they appear to be reported.
Which characteristic of data is a measure of the amount that the data values vary?
Variation
Does the frequency distribution appear to have a normal distribution? Explain. Temperature (°F) 35-39 40-44 45-49 50-54 55-59 60-64 65-69 Frequency 1 4 9 15 9 2 1
Yes, because the frequencies start low, proceed to one or two high frequencies, then decrease to a low frequency, and the distribution is approximately symmetric.
Let the frequencies be substantially different if any frequency is at least twice any other frequency. Does it appear that these births occur on the days of the week with equal frequency? Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 52, 66, 68, 55, 63, 44, 52.
Yes, it appears that births occur on the days of the week with frequencies that are about the same.
Class width is found by _______.
subtracting a lower class limit from the next consecutive lower class limit