Statistics Homework

Statistics Homework
To estimate the distance from your home, some common measures may include (a) hours (b) miles (c) kilometers.
When comparing using ‘miles’ with ‘hours’ to measure distance, which one is better? Give at least two reasons.
Miles is a better measure of distance when compared to hours. That is because it is a true measure of the distance and is not dependent on other factors. On the other hand, time is a relative measure for distance since it is dependent on speed and the actual distance between the two points.
When comparing ‘miles’ with ‘kilometers’, which one is better? Give your reason.
Kilometers is a better measure of distance than miles. That is because kilometers is the most commonly used standard measure for distance across the world. Miles is used as a standard measure for distance in only a few countries to include the USA. As such, using the kilometer makes the results more understandable to a larger audience.
For this project, what would be the target population?
For this project, the target population is the students with the intention of determining the distance between the students’ homes and the university campus.
Questions on the contents from Chapter 1, 2, 3
If a student is from Canada and gave the estimate as 800 kilometers, and he recorded 800 as his distance. There is clearly a measuring unit problem. What should be the correct data value for his distance in miles?
1 kilometer equates to a distance of approximately 0.6214 miles. A distance of 800 kilometers would be equal to 497.

1 miles. As such, the correct data value for the distance in miles is 497.1 miles.
Use the Distance Data to answer the following questions:
The type of Data collected here is (observational or experimental?) Observational data was collected
List two Qualitative or Categorical Variables in this data set: Gender, grade and region are qualitative variables.
Is the variable ‘Right-distance’ a nominal scale or ordinal scale? It is a nominal scale and not an ordinal scale and Why? That is because it has labelled the variable without any numerical significance.
Is the variable, ‘Miles’ continuous or discrete? It is continuous and Why? That is because it can occupy any value from one onwards.
Is the variable ‘Miles’ Interval scale or Ratio scale? It is an interval scale and Why? That is because the exact distance between the values is known and the same such that a 1-mile difference is the same across all distance.
If you compute the average distance using these data values, is this average distance a (i) ‘parameter’ or a (ii) ‘statistic’? ANS: Statistic and Why? It is a statistic (and not a parameter) because the average distance summarizes distance for a sample, as a population subset, and not the whole population.
Think of three possible non-sampling errors in collecting this data:
There are three possible non-sampling errors. Firstly, there was a possibility of data entry errors since the data was collected for 200 respondents, which may have caused a problem with transcribing. Secondly, there is a possibility that some of the respondents offered false information with the researcher having no way of ascertaining if the information was true or false. Finally, an error may be haven brought about by using an inaccurate sampling frame.
In this project, we collect the data from this class. Is this a representative sample of the target population? Give your reason.
This is not a representative sample of the target population. This is because it covers only one class and does not include representatives from other classes. To collect data that represents the whole school population, the researchers should have provided all the students with an opportunity to engage in the research as respondents.
Descriptive information and graphical displays of the top three reasons coming to the University
Use table to summarize the frequency of ‘reasons’ for choosing the University. What are the top three reasons:
Top Reason Frequency out of 200 students? %
1 Right distance 116 58
2 Reputation 85 42.5
3 Size 77 38.5
For the top reason you found in (a), fill the follow table to find out the frequency and % of males and females students chose this top reason:
Top Reason
Yes (give frequency and % ) No (frequency and %) Total (frequency)
Female 48 (24%) 31 (15.5%) 79 (39.5%)
Male 68 (34%) 53 (26.5%) 121 (60.5%)
Total (Frequency) 116 (58%) 84 (42%) 200 (200%)
Draw a Bar Graph for the Reason ‘Right_Distance’ for Female and Male, separately, but, on the same graph.

How many % of females choose ‘Right_Distance (‘Yes’ (=1) ) as their reason: 60.76% (48/79)
How many % of males chooses ’Right_distance’ as their reason: 56.2% (68/121)
Draw a Pie graph for the ‘Grade’ variable to see the % of students in each grade level.

What is the % of Senior students in this data? 20.5% (41/200)
Construct a histogram for variables ‘Miles’ and ‘Miles_1’ respectively.

Describe the shape of ‘ Miles’ distribution: The distribution has stretched spread in terms of scatter, variability and dispersion since it covers a wider range.
Describe the shape of ‘ Miles_1’ distribution: The distribution has squeezed spread in terms of scatter, variability and dispersion since it covers a narrower range.
Comparing the Average Distances between ‘Miles’ and ‘Miles_1’ without computing the averages, which one has larger average? Why?
Miles_1 has a greater average distance when compared to Miles. That is because Miles includes distances greater than 1,000 miles which push the average up. On the other hand, Miles_1 does not have any distance greater than 1,000 miles thereby bringing its average down.
Comparing the Median Distances between ‘Miles’ and ‘Miles_1’ without computing the medians, are two medians very different or very close? Why?
The two medians are very close. That is because Mile_1 has 198 values while Miles has 200 values. There is only 8 values separating the two thereby ensuring that the median difference between the two is very close.
6. Construct a histogram of the variable Miles_1 for male and female, separately, on the same graph in different panels.

Compare the shapes of the distributions for the Miles_1 between Female and Male students:
A review of the shapes of the distributions shows that while the females have a normal distribution, the males have many outliers.
Which one is more skewed (Female or Male distribution): Males distribution
(c ) Which distribution (Male or Female) of Miles_1 shows larger variation: Males distribution
7. Obtain the following summaries for Miles and Miles_1.
Variable N Mean Std Median Q1 Q3 Min Max Range IQR
Miles 200 362.5319 1444.407 110 50 150 0 9999.99 9999.99 100
Miles_1 192 107.9813 97.70857 105 50 145 0 996 996 95
(a) Compute an estimate of standard deviation, s, for Miles_1 using Range/6 = 996/6 = 166
How close is this estimated s to the actual standard deviation of Miles_1:
Estimate s.d./Actual s.d. = 166/97.71 = 1.7
Suppose a student has the Distance of 40. Use the Empirical Rule based on the information of ‘Miles_1 variable to decide if this is an unusual Distance or not.
The standard deviation is 97.71 while the mean is 107.98. A distance of 40 miles is within 1 standard deviation of the mean to imply that it falls within 68% of the collected values. This is not an unusual distance.
(d) Suppose a student has the Distance of 300. Compute the corresponding Z-score and using the Empirical rule to decide if this is an unusually far distance away from home or not.
Z score = (data-mean)/standard deviation = (300-107.98)/97.71 = 1.97. Applying the empirical rule to this figure shows that it falls within 68% of the values, to imply that it is not an unusually far distance away from home.
8. Obtain the following summaries for Miles_1 for Males and Females separately.
Variable Gender N Mean Std Median Q1 Q3 Min Max Range IQR
Miles_1 Female 76 106.1789 82.60982 105 49.25 150 0 550 550 100.75
Male 116 109.1621 106.7803 106.5 50 140.75 0 996 996 91.5
9. Construct the box plot for the variable Miles_1.
9a) Based on the box plot, what is the shape of the distribution of the Miles_1?
The boxplot indicates that there are more figures found in the male gender when compared to the female gender. In addition, the distribution shows that the males have the highest figure, with the meal being almost equal.
9b) Is there any outliers based on this boxplot?
The boxplot shows that there are outliers found among the higher figures.
10. Construct a box plot of the variable Miles_1 for male and female, separately, on the same graph in different panels and paste them here. Based on the box plots and the dot plots, describe the distributions of Miles_1 for Female and Male, respectively.