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Mathematics 215 – Assignment 1

Mathematics 215 – Assignment 1

1. Observations from the first 25 days of the year showed that the following number of pedestrians used a particular crosswalk on each day:
191322578621018432997143566481596743971059131667687125

(8marks)
a. Construct a frequency distribution for this using a lower limit for the first class of 15 and a class width of 20. Indicate the class limits, boundaries, midpoints, frequencies and cumulative frequencies.

(4marks)
b. Create a relative frequency polygon of the number of pedestrians.

(4marks)
c. Create a percentage ogive of the number of pedestrians.

(3marks)
d. Calculate the approximate value of the 30th percentile. What does this number tell you?
(3marks)
e. Circle True (T) or False (F) for each of the following statements with reference to the original dataset information given in this question.
T F The number 132 represents an element.
T F The information provided represents the use of cross-section data.
T F The number of pedestrians is a continuous variable.
(4marks)
2. Indicate whether each of the following examples describes the use of descriptive (D) or inferential (I) statistics by clearly circling D or I.
D I In my son’s grade-three classroom, 25% of the kids are under the age of eight and 75% are eight or older.
D I A comparison between placebo and drug treatments has determined that drug X produces approximately a 5% reduction in the severity of symptoms of Alzheimer’s patients.
D I A non-leap year consists of 525,600 minutes.
D I By examining the browsing habits of individuals last week, a well-known Internet retailer has estimated that 13% of those people who visit their website will make a purchase.
(5marks)
3. An average glass of milk contains 115 grams of calcium with a standard deviation of 8 grams. Using Chebyshev’s theorem, construct an that contains the calcium content of at least 50% of the glasses of milk.
Retain 2 decimal places of accuracy in all calculations.

(11total marks)
4. The monthly cell phone bills for 100 senior citizens are summarized in the following frequency distribution table:
Cell Phone Bill (in dollars) Frequency
10 to less 20   1
20 to less 30   9
30 to less 40  10
40 to less 50  26
50 to less 60  43
60 to less 70  11
Total 100
(3marks)
a. Using the frequency distribution table, calculate the mean cell phone bill amount.Note: You may add columns to the table to assist you with your work.
(3marks)
b. Using the frequency distribution table, and treating the as population , calculate the standard deviation of cell phone bill amount.Note: You may add columns to the table to assist you with your work.
(2marks)
c. Estimate the class range that contains the median cell phone bill amount.
(2marks)
d. Does the appear to be skewed? If yes, in what direction? Describe how you came to this conclusion.
(1mark)
e. Circle True (T) or False (F) for the following statement:
T F Selecting 100 senior citizens out of 500 who live in a particular town in order to calculate the mean cell phone bill of seniors in the town is an example of sampling without replacement.
(33total marks)
5. The following represents the number of cigarettes smoked per day for a sample of 18 teenagers, each of whom identifies as a smoker:
26 15 21 26 9 31 20 30 21 0 19 25 16 32 14 27 28 18

(4marks)
a. Construct a stem-and-leaf display for this . Place the leaves in ascending order.
(2marks)
b. What is an advantage of using a stem-and-leaf display for this as compared to a histogram?
(2marks)
c. Calculate the mean number of cigarettes smoked.
(7marks)
d. Calculate the standard deviation and coefficient of variation for the number of cigarettes smoked.
(5marks)
e. Calculate the quartiles and interquartile range for this .
(5marks)
f. Sketch a box-and-whisker plot on the paper below. Indicate any outliers.

(2marks)
g. What is an advantage of representing the using a box-and-whisker plot as compared to a stem-and-leaf display?
(3marks)
h. What is the percentile rank of a teenager who smokes 31 cigarettes per day? What does this number tell you?
(3marks)
i. Circle True (T) or False (F) for each of the following statements with reference to the sample information given in this question:
T F If the sample of teenagers is selected in a way that ensures that each teenager has an equal chance of being selected, this is called a simple random sample.
T F The fact that the mean number of cigarettes smoked per day for the sample will differ from the population mean number of cigarettes smoked per day, because the sample is a subset of the population, leads to a non-sampling error.
T F If the sample of 18 teenagers is selected in a way that ensures that 9 of the teenagers are randomly selected from the male smokers and the 9 teenagers are randomly selected from the female smokers, this is an example of systematic random sampling.
These extra are for additional calculations. If you need them for your solutions, please reference them in the appropriate place in the questions.

$20.00

Mathematics 215 – Assignment 1

$20.00