Elementary Statistics, Chapter 2, Unit 1, Homework Problems

Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant​ criteria?

No, the distribution does not appear to be normal. (I don't get this, so come back to it)

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.

The sum of the relative frequencies is 124%, but it should be 100%, which 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.

A frequency table of grades has five classes​ (A, B,​ C, D,​ F) with frequencies of 5​, 10​, 18​, 5​, and 3 respectively. Using​ percentages, what are the relative frequencies of the five​ classes?

(divide a frequency (like 5) by the sum of frequencies, 41 and then multiply that by 100.) 12.20%, 24.39%, 43.90%, 12.20%, 7.32%

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. Does the frequency distribution appear to be roughly a normal​ distribution?

22, 4, 3, 0, 0, 0, 1 No, the distribution is not symmetric and the frequencies do not start off low.

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.

3, 9, 4, 3, 1 (easy)

Refer to the accompanying data set and use the 30 screw lengths to construct a frequency distribution. Begin with a lower class limit of 3.470 ​in., and use a class width of 0.010 in. The screws were labeled as having a length of 3 1/2 in.

3.470-3.479, 3.480-3.489, 3.490-3.499, 3.500-3.509, 3.510-3.519 2, 6, 10, 10, 2

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?

48 individuals are included in the summary (add up all numbers in the frequency column) No. The data values in each class could take on any value between the class​ limits, inclusive.

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. Based on the​ distribution, do the weights appear to be reported or actually​ measured? What can be said about the accuracy of the​ results?

8, 2, 2, 1, 3, 10, 1, 0, 3, 1 The weights appear to be reported because there are disproportionately more 0s and 5s. They are likely not very accurate because they appear to be reported.

Does the frequency distribution appear to have a normal​ distribution? Explain.

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.

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. Blood Platelet Count of Males (1000 cells/uL): 0-99, 100-199, 200-299, 300-399, 400-499, 500-599, 600-699 Frequency: 3, 49, 76, 25, 0, 1, 0

lower class limits: 0, 100, 200, 300, 400, 500, 600 upper class limits: 99, 199, 299, 399, 499, 599, 699 class width: 100 class midpoints: 49.5, 149.5, 249.5, 349.5, 449.5, 549.5, 649.5 class boundaries: -0.5, 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5 number of individuals: 154

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. Blood Platelet Count of Females (1000 cells/uL): 100-199, 200-299, 300-399, 400-499, 500-599 Frequency: 26, 93, 26, 1, 2

lower class limits: 100, 200, 300, 400, 500 upper class limits: 199, 299, 399, 499, 599 class width: 100 class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5 class boundaries: 99.5, 199.5, 299.5, 399.5, 499.5, 599.5 number of individuals: 148

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: 25-34, 35-44, 45-54, 55-64, 65-74, 75-84, 85-94 Frequency: 29, 34, 16, 3, 5, 1, 2

lower class limits: 25, 35, 45, 55, 65, 75, 85 upper class limits: 34, 44, 54, 64, 74, 84, 94 class width: 10 (34-25+1) class midpoints: 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5 class boundaries: 34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5 (don't forget to find the lowest class boundary which is 24.5) number of individuals included included in the summary: 90

Class width is found by ____________.

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

True or false: Outliers are sample values that lie very far away from the majority of the other sample values.

true

True or false: Variation is a measure of the amount that the data values vary.

true