Question

Kentucky Derby The following data set shows the winning times (in seconds) for the Kentucky Derby races from 1950 to 2007 . a. Do you think there will be a trend in the winning times over the years? Draw a line chart to verify your answer. b. Describe the distribution of winning times using an appropriate graph. Comment on the shape of the distribution and look for any unusual observations.

Short answer

Question: Analyze the trend and distribution of Kentucky Derby winning times between 1950 and 2010. Describe the shape of the distribution and identify any unusual observations.

Step-by-step solution

Understand what a trend is

A trend is a long-term pattern that indicates a general direction in which a set of data is moving. In this case, we want to understand if there is a trend in the winning times of the Kentucky Derby races from 1950 to 2010.

Draw a line chart

To draw a line chart, you'll need to plot the Year on the x-axis and the winning times on the y-axis. Then connect the data points with a line. Remember that for this exercise, we don't have the data set, so you need to get the data set first. Once the line chart is drawn, you'll be able to analyze whether there is a trend in the winning times over the years.

Describe the distribution of winning times

To describe the distribution, you can use an appropriate graph such as a histogram or a box plot. A histogram will display the frequency of winning times against the winning time intervals, whereas a box plot will show the median, quartiles, outliers, and minimum and maximum values. Choose a graph based on the given data set and create it to describe the distribution of winning times.

Discuss the shape of the distribution

Once you have drawn the histogram or box plot, analyze the shape of the distribution. Look for features such as symmetry, skewness, or any patterns. A symmetric distribution will have its mean, median, and mode close to each other, while a skewed distribution will have either a long tail towards the positive side (right-skewed) or the negative side (left-skewed).

Identify any unusual observations

Analyze the previous steps' graphs to look for unusual observations or outliers. These are data points that are very different from the typical values in the distribution. If there are outliers, investigate the reasons behind them and whether they have any impact on the overall trend and distribution of winning times. By following these steps, you should be able to answer both parts of the exercise and provide a robust analysis of the trend and distribution for Kentucky Derby winning times between 1950 and 2010.

Key concepts

Line Chart

A line chart is a powerful tool for visualizing data across a time series. It's particularly useful for spotting trends.
To create a line chart for the Kentucky Derby winning times, you will first plot the years on the x-axis. Then, place the corresponding winning times on the y-axis. Connect these points with a line.
This line helps to clearly illustrate any upward or downward trends over time.

• If the line consistently moves in one direction, it indicates a trend. An upward trend implies increasing winning times, while a downward trend indicates they are decreasing.
• Seeing the line flat or moving with no particular direction might suggest stability or no trend.

Line charts make comparing changes over different periods straightforward and effective.

Distribution

In data analysis, understanding the distribution of data helps identify patterns or anomalies.
The distribution is a statistical term that describes the way data points are spread out.

• A critical characteristic of a distribution is its shape, which can be symmetric, skewed, or even uniform.
• The shape can inform you of the typical values that occur more frequently.

Graphically, distributions are commonly depicted with histograms or box plots, both of which aid in visualizing the spread and shape of data.

Histogram

A histogram is a type of bar graph that is used to represent the distribution of numerical data. It divides the data into intervals called bins.
When creating a histogram for the Kentucky Derby winning times, each bar will represent the number of races that fall within a specific range of winning times.

• The height of each bar indicates the frequency of winning times within that interval.
• By examining the histogram, you can quickly determine where most winning times are clustered.

The histogram gives a good overview of how data points are distributed, making it easier to spot any skewedness or irregularities such as outliers.

Box Plot

A box plot, also known as a whisker plot, is a graphic representation of data that shows the data's central tendency, spread, and symmetry.
It is particularly useful in identifying outliers.
In a box plot for the Kentucky Derby winning times, you'll notice several key components:

• The central box spans from the first quartile (Q1) to the third quartile (Q3), effectively highlighting the middle 50% of the data.
• The line inside the box denotes the median, giving insight into the central value of the data.
• Lines (whiskers) extend from the boxes to the minimum and maximum, showing the full spread of data.
• Any dots outside the whiskers indicate outliers, which are significant deviations from the majority of data points.

Box plots are invaluable for revealing the overall variability in dataset distribution and pinpointing unusual data points.