Introductory Statistics for Laboratorians dealing with High Throughput Data sets Centers for Disease Control

Problem 1 Spelling Test Scores: 5, 6, 10, 8, 8, 4, 5, 5, 9, 8, 6, 6, 7, 4, 5, 5, 5, 3, 6, 9 How many kids took the test? What is the lowest and highest score? Tally the scores on the table provided.

Frequency Table Score X TallysFrequency

Questions How many kids scored 5 on the test? How frequently did the score 10 occur? What is the frequency of the score 3? What is the frequency of X = 8? What was the most frequent score?

Definitions Scores are called X. The most frequent score is the Mode. The number of times the score occurs is called the frequency of that score. The Table is called a frequency distribution.

Problem 2 A checklist of 8 symptoms of the disease is developed. People are scored by counting how many symptoms they check X is the number of symptoms the person checks

Problem 2 Score X Frequency f

Questions How many people checked all 8 symptoms? How many checked 5 symptoms? How many checked 4 symptoms? How many people were in the study (total)? Using the axis provided make a histogram of the data. Using the axis provided make a line graph of the data.

Frequency Distribution

Bar Chart

Line Graph

Problem 3 Score X Frequency F How many people were in the study (total)? What percent of the people scored 8 or less? What percent scored 5 or less? What percent scored 1 or less?

Definitions The proportion that falls at or below a particular score is the number of people at or below that score divided by the total number of people. The percentage that falls at or below a particular score is the proportion times 100.

Fill in the Proportions and Percentiles Score X Frequency F PercentileProportion

Problem 4 Write the 50 scores in Problem 3 on the cards provided and drop them in a hat. Shake them up or shuffle them to randomize them.

Hint Here are the 50 scores: 8,8,8,8,7,7,7,7,6,6,6,6,6,6,6,6,6,6,6,5,5,5,5,5,5, 5,5,5,5,4,4,4,4,4,4,4,4,4,4,3,3,3,3,2,2,1,1,1,0,0

Probability Score X Frequency fPercentageProportion Number at or below Cf If I put these 50 scores in a hat and draw one out at random, what are the chances that the number I draw will be 8 or less? What are the chances it will be 4 or less? What are the chances it will be 1 or less?

Definition The probability of being at or below a particular score in a distribution is the proportion of the distribution that is at or below that score.

Problem 5 Score X Frequency f Total10 Make a Bar Chart for this frequency distribution.

Probabilities from Areas

Count the red and black blocks to compute the proportions. What proportion of the distribution is at or below 4? What proportion of the distribution is at or below 2?

Probabilities from Areas Works the same way for a histogram If each square is a square inch, then The probability of being at or below a particular score is the number of square inches at or below that score divided by the total number of squares.

Compute the Probability If we write these 10 scores on cards and draw one at random: What is the probability of being at or below 4? What is the probability of being at or below 2? What is the probability of being between 2 and 4 (ie: greater than 2 and 4 or less)?