Reading Statistical Data

Objective When you have large sets of data it helps to look at it using statistical forms. These are commonly histograms that show how the data points are distributed not across time, but by density. This lesson will assist in constructing graphs which in turn will assist in conceptualizing the graphs. Register

The Mission Four riders are preparing for the first bike race of the season. Their coach, wants to predict who is going to do the best at this weekend’s race. Each of the riders uses a power meter on their bike that records ride time, distance, speed, heart rate, and power. We have also provided each rider’s weight as heavier riders do usually put out more power than smaller riders. Using data from their last five rides in Microsoft Excel predict who will have the best chance at success in the race.

Coach begins the statistics Mean M edian Mode The sum of a set of numbers divided by the amount of numbers The number that occurs most frequently. The middle number if you counted towards the middle from the first and last number To begin designing graphs, you must first calculate the necessary statistics to be able to understand the data. Together, these statistics are referred to as the Central Tendency. The coach inputs the data into an excel sheet to make the calculations easier.

The following short video will outline how to use the Excel data we’ve prepared for you Files: – Vance Legstrong Vance Legstrong – Freddy Merckx Freddy Merckx – Padel Bevans Padel Bevans Using Excel to Manage the Riders’ Data

Calculating the Mean =AVERAGE(*Insert Range of Cells*) For example: =AVERAGE(B1:B20) for a column of 20 rows Or: =AVERAGE(A4:J4) for a row across10 columns Mean is the sum of a set of numbers divided by the amount of numbers. The mean is also referred to as the average of a set of numbers Given a rider’s speed in Km/h at six different times on the ride: 5, 10, 12, 12, 8, 3 The mean would be: ( )/6 = 833 Km/h All the numbers are added together, then divided by the amount of numbers (6 for this example) Compared to the other measures of central tendency, the mean is normally the most accurate. However, it is important to know that if the data is skewed in a direction, the mean will increase or decrease. This will be examined later when we discuss graphs Definition: Simple Example: Why mean is useful: Excel function:

Calculating the Median =MEDIAN(*Insert Range of Cells*) For example: =MEDIAN(B1:B20) for a column of 20 rows Or: =MEDIAN(A4:J4) for a row across10 columns The middle number if you counted towards the middle from the first and last number. If you have a range of values, the median is the middle number Given a rider’s speed in Km/h at six different times on the ride: 5, 10, 12, 12, 8, 3 The median would be In this case the median falls between two numbers. The average can be taken between these numbers, but between 8 and 10 is simply 9. Next to mean, median can be the most accurate, provided you have a normal curve. Median is still effected by skew, though not as much as mean can be. This will be examined later when we discuss graphs Definition: Simple Example: Why median is useful: Excel function:

Calculating the Mode =MODE(*Insert Range of Cells*) For example: =MODE(B1:B20) for a column of 20 rows Or: =MODE(A4:J4) for a row across10 columns The number in a set that occurs with the greatest frequency. Given a rider’s speed in Km/h at six different times on the ride: 5, 10, 12, 12, 8, 3 The mode would be 12, because it is the only number that occurs more than once. Mode is not necessarily an accurate measure of central tendency and is very poor in small samples of evidence. Importantly though, the mode (frequency) is reported in Histograms. This will be examined later when we discuss graphs Definition: Simple Example: Why mean is useful: Excel function:

Coach begins the graphs Histogram Time-based View A bar graph that shows how frequently data occur within a certain range. Used to compare large sets of data and see how frequently certain levels of data occur A chronological graph of data from the start of something to the end Used to examine changes over time Coach must design the graphs necessary to analyze the data. He must first decide which graph will best represent his data.

Histogram Click to have the description of the term appear X-axis Y-axis The x-axis is the variable to be measured In this case, heart-rate is the x-axis The y-axis is always a measure of count, how often the data is at that level In this case, the heart-rate is most often between

Time-based View Click to have the description of the term appear X-axis Y-axis The x-axis is always time in a time based view. This shows the progression of time on the y-axis The y-axis is the variable to examine over time. In this case, heart-rate is the y-axis

Histogram When to use: Advantages: Disadvantages:

Time-based view When to use: Advantages: Disadvantages:

The assistant coach needs help Mean M edian Mode The assistant coach still has difficulty calculating the statistics needed to judge performance. Match the measure with its definition C. The sum of a set of numbers divided by the amount of numbers A. Number in the middle of the range B. Number that occurs most frequently