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Descriptive Statistics Report - Project Part 3

I. Introduction

My group and I designed a four-question survey to learn whether texting while driving was causing accidents and, if so, how many.  We looked at age and gender as part of this survey, as well how often drivers texted in a 24-hour period; we also surveyed the number of accidents among drivers who reported them.  We surveyed all drivers, regardless of age.  Instead of a random survey, we polled our coworkers, family, friends, friends of friends, and friends of family.  We have a convenience survey and voluntary responses.  We used phone, email, and face-to-face surveys to obtain our results.

We asked the following questions:

1.  Are you male or female?

2.  What is your age?

3.  How often do you text while driving in a 24-hour period?
a.  0 times
b.  1-5 times
c.  6-10 times
d.  >10 times

4.  How many accidents have you had while texting and driving?

II.  Looking at a Categorical Variable

The responses to the question "How often do you text while driving in a 24-hour period?" are shown in the pie chart below.

Result 1: Pie Chart of frequency of texting and driving   [Info]

Among drivers of all ages, the majority, or 43.87%, do not text and drive. Almost 22% (or 21.94%) text 1-5 times in a 24-hour period; 16.13% text 6-10 times in a 24-hour period, and 18.06% text greater than 10 times in a 24-hour period.

In order to see if the frequency of texting and driving differs between male and female drivers, we can examine the bar plot below.

Result 2: Frequency of driving and texting for male and female drivers   [Info]

Among both male and female drivers, the most frequent choice is not to text and drive.  Among drivers that text and drive, females are more likely than males to text 0-5 times within a 24-hour period. They are also more likely than males to text 6-10 times within a 24-hour period.  Male drivers are more likely to text >10 times within a 24-hour period.

III. Looking at a Numerical Variable

The responses to the question, "What is your age" are shown in the histogram, box plot, and summary statistics below.

Result 3: Histogram of age of drivers   [Info]

Result 4: Boxplot of ages of drivers   [Info]

Result 5: Summary statistics for age of drivers   [Info]
Summary statistics:
Column n Mean Variance Std. dev. Median Range Min Max Q1 Q3
AGE 155 38.045161 205.82262 14.34652 34 69 17 86 27 47

The histogram shows a right-skewed distribution with the majority of the data (drivers) less than 50 years of age.  The median represents the value in the exact middle of the data; it is best used when data is skewed. The median here is 34 years of age, while the mean is about 38 years of age.  A mean greater than the median is typical with right-skewed distribution. The histogram midrange (86+17)/2 is 51.5, which is not a reasonable measure of center for this data (see histogram).

With a range of 69 and a standard deviation of 14.35, there is a great deal of variability of this data of the ages of drivers.  The IQR, or middle range of the data, is 20 years of age (IQR = Q3 - Q1).  The range rule of thumb (range/4 = 17.25) is not a good approximation of the standard deviation, which is 14.35.  Because the data is right skewed and there are outliers, the range/4 overestimates the standard deviation.

The boxplot of ages of drivers reveals two outliers, 85 and 86, which I determined by sorting the data; they lie outside the values of most of the data.  These values represent drivers of ages 85 and 86, which is plausible for active elderly adults who still drive; I believe them to be legitimate data values.  In addition, when I calculated quartiles (Q1 and Q3) and interquartile range, 85 and 86 did not meet the data values necessary to be outliers (Triola, p. 121).

IV. Looking for a Relationship between Two Numerical Variables

To determine whether or not there is a relationship between the responses to the questions "What is your age?" and "How many accidents have you had while texting?", we looked at the scatter plot of the survey response data from these two questions.

Result 6: Scatter plot for age of driver and number of accidents while texting   [Info]

The scatterplot follows a negative direction, decreasing as it moves from right to left.  The scatter in the plot is spread in three different areas depending on the number of accidents and ages of drivers at the time surveyed. The majority of drivers had no accidents regardless of age.  When accidents occured, the majority occured between 20 and 30, with no accidents after age 50.  One driver in the 20-30 age range had two accidents; other drivers who reported accidents had only one.

The correlation coefficient for the paired data (number of accidents with age of driver) is approximately -0.139, as shown below. The absolute value of r (0.139) is less than 0.196 (table A-5 in Triola textbook); there is a weak linear correlation between the number of accidents and the age of drivers.

Result 7: Correlation between number of accidents and age of driver   [Info]
 Correlation between ACCIDENTS and AGE is:-0.13852329

Data set 1. PROJECT 1 Katy Holloway (group)   [Info]