Sections 2.1 & 2.2 Homework

Age(years) of Best Actress when award was won Frequency 20-29 26 30-39 35 40-49 15 50-59 3 60-69 5 70-79 2 80-89 2

Age​ (years) of Best Actress when award was won Cumulative Frequency Less than 30 26 Less than 40 61 Less than 50 76 Less than 60 79 Less than 70 84 Less than 80 86 Less than 90 88

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, 29.2, 19.2, 28.2, 33.5, 23.7, 23.2, 44.9, 26.5, 18.3, 24.7, 31.5, 23.5, 27.4, 37.7, 29.2, 25.3, 24.9, 33.8, 25.8

Body Mass Index Frequency 15.0-20.9 3 21.0-26.9 8 27.0-32.9 5 33.0-38.9 3 39.0-44.9 1

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 54​, 65​, 71​, 59​, 53​, 46​, 52. Does it appear that such births occur on the days of the week with equal​ frequency?

Day Relative Frequency Monday 13.5​% Tuesday 16.25​% Wednesday 17.75​% Thursday 14.75​% Friday 13.25​% Saturday 11.5​% Sunday 13.0​% ​Yes, it appears that births occur on the days of the week with frequencies that are about the same.

A​ _______ helps us understand the nature of the distribution of a data set.

Frequency distribution

A frequency table of grades has five classes​ (A, B,​ C, D,​ F) with frequencies of 3​, 15​, 15​, 8​, and 2 respectively. Using​ percentages, what are the relative frequencies of the five​ classes?

Grade Frequency Relative frequency A. 3 6.98​% B. 15 34.88​% C 15 34.88​% D 8 18.60​% F 2 4.65​%

Identify the lower class​ limits, upper class​ limits, class​ width, class​ midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary. Age (yr) when award was won Frequency 15 - 24 29 25 - 34 36 35 - 44 16 45 - 54 2 55 - 64 6 65 - 74 2 75 - 84 1

Identify the lower class limits. 15 ​,25 ​,35​, 45, 55​, 65​, 75 Identify the upper class limits. 24, 34​, 44​, 54​, 64​, 74​, 84 Identify the class width. 10 Identify the class midpoints. 19.5, 29.5​, 39.5​, 49.5​, 59.5​, 69.5​, 79.5 Identify the class boundaries. 14.5​, 24.5​, 34.5​, 44.5​, 54.5​, 64.5​, 74.5​, 84.5 Identify the number of individuals included in the summary. 92

The table below shows the frequency distribution of the rainfall on 52 consecutive Thursdays in a certain city. Use the frequency distribution to construct a histogram. Do the data appear to have a distribution that is approximately​ normal? is approximately​ normal? Class Frequency 0 −0.19 21 0.20−0.39 13 0.40−0.59 5 0.60−0.79 2 0.80−0.99 9 1.00−1.19 1 1.20−1.39 1

No, it is not symmetric.

_______ are sample values that lie very far away from the majority of the other sample values.

Outliers

The last digit of the heights of 3838 statistics students were obtained as part of an experiment conducted for a class. Use the following frequency distribution to construct a histogram. What can be concluded from the distribution of the​ digits? Specifically, do the heights appear to be reported or actually​ measured? Digit. Frequency 0 3 1 3 2 5 3 3 4 4 5 5 6 4 7 3 8 3 9 5

The data appears to be measured. The heights occur with roughly the same frequency.

The normal quantile plot shown to the right represents duration times​ (in seconds) of eruptions of a certain geyser from the accompanying data set. Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution.

The distribution is not normal. The points are not reasonably close to a straight line.

If we collect a large sample of blood platelet counts and if our sample includes a single​ outlier, how will that outlier appear in a​ histogram?

The outlier will appear as a bar far from all of the other bars with a height that corresponds to a frequency of 1.

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) Relative Frequency 130 - 144 22% 145 - 159 25% 160 - 174 23% 175 - 189 28% 190 - 204 27%

The sum of the relative frequencies is 125​%, but it should be​ 100%, with a small possible​ round-off error. Your answer is correct. 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.

Which characteristic of data is a measure of the amount that the data values​ vary?

Variation

Refer to the accompanying data set and use the 25 home voltage measurements to construct a frequency distribution with five classes. Begin with a lower class limit of 127.2 ​volts, and use a class width of 0.2 volt. Does the result appear to have a normal​ distribution? Why or why​ not?

Voltage​ (volts) Frequency 127.2−127.3 2 127.4−127.5 6 127.6−127.7 9 127.8−127.9 7 128.0−128.1 1 Yes, because the frequencies start low, reach a maximum, then become low again, and are roughly symmetric about the maximum frequency.

Refer to the table summarizing service times​ (seconds) of dinners at a fast food restaurant. How many individuals are included in the​ summary? Is it possible to identify the exact values of all of the original service​ times? Time (sec) Frequency 60 - 119 8 120 - 179 24 180 - 239 16 240 - 299 1 300 - 359 6

55 No. The data values in each class could take on any value between the class​ limits, inclusive.

The population of ages at inauguration of all U.S. Presidents who had professions in the military is​ 62, 46,​ 68, 64, 57. Why does it not make sense to construct a histogram for this data​ set?

With a data set that is so​ small, the true nature of the distribution cannot be seen with a histogram.

The frequency distribution below represents frequencies of actual low temperatures recorded during the course of a​ 31-day month. Use the frequency distribution to construct a histogram. Do the data appear to have a distribution that is approximately​ normal? Class Frequency A 39−44 1 B 45−50 2 C 51−56 6 D 57−62 12 E 63−68 6 F 69−74 2 G 75−80 2

Yes, it is approximately normal.

Heights of adult males are normally distributed. If a large sample of heights of adult males is randomly selected and the heights are illustrated in a​ histogram, what is the shape of that​ histogram?

bell-shaped

The histogram to the right represents the weights​ (in pounds) of members of a certain​ high-school debatedebate team. How many team members are included in the​ histogram?

class width: 20 lower class: 110 upper class: 130

The heights of the bars of a histogram correspond to​ _______ values.

frequency

​A(n) _______ distribution has a​ "bell" shape.

normal

In a​ _______ distribution, the frequency of a class is replaced with a proportion or percent.

relative distribution

A​ _______ histogram has the same shape and horizontal scale as a​ histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies.

relative frequency

Class width is found by​ _______.

subtracting a lower class limit from the next consecutive lower class limit

Bars on a histogram ___.

touch

Does the frequency distribution appear to have a normal​ distribution? Explain. Temperature_(F) Frequency 35-39 1 40-44 3 45-49 9 50-54 14 55-59 9 60-64 4 65-69 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.