DATA ANALYSIS: STATISTICS AND GRAPHING LAB 2 DATA ANALYSIS: STATISTICS AND GRAPHING

OBJECTIVES Learn to use descriptive statistics: mean, standard deviation, median, mode, and range Proper graphing techniques Learn to use Excel to analyze circadian rhythm data

DESCRIPTIVE STATISTICS Mean: the average of a group of measurements. - Add all the values in a data set and divide that number by the total number of values. Median: the middle value of a group of measurements. - Arrange all values from the smallest to largest and the middle number is consider the median. Mode: the value that occurs the most frequently in a data set. Range: the difference between the highest and lowest values. Standard Deviation: indicates how measurements vary around the mean. - Calculate the mean, measure the deviation of each sample from the mean, square each deviation, and then sum all deviations. Use this number and divided by the number of samples minus “one” and finally square this number.

EXAMPLE Students Quiz 1 scores: 9,7,8,10,5,6,7,4,8,7 Mean: 9+7+8+10+5+6+7+4+8+7 / 10 = 71/10 = 7.1 Median: 4, 5, 6, 7, 7, 7, 8, 8, 9, 10 Middle Number: 7 Mode: 7 (the most frequent value) Range: 10 – 4 = 6

EXAMPLE Standard Deviation: Sum of all squared deviations = 29 / 10 quiz values – 1 = 29/9= 3.22 Square root of 3.22 = 1.79 The mean of Quiz 1 was 7 +- 1.79 Quiz Score Mean Deviation (Deviation)2 9 7 2 4 8 1 10 3 5 -2 6 -1 -3

PROPER GRAPHING TECHNIQUES A graph needs to have: Title Date Axes should be clearly labeled including units The most common graph is called histogram. This graph visually display the frequency distribution of data. - Absolute frequency: the number of times a value occurs in a data set. - Relative frequency: used to compared two or more data sets where the number of values obtained is not equal. This is calculated by dividing the absolute frequency by the total number of values. This number is then multiplied by 100%.

EXCEL In the lab, you will be using the class data on “height” collected in the previous week’s lab to practice calculating descriptive statistics and graphing the absolute frequencies of the heights of Biology 2425 students using Excel. You will also be using the “age” data collected last week to calculate descriptive statistics and graphing the relative frequencies of ages of Biology 2425 students using Excel.

ANALYZING DATA Measurements that are both accurate and precise are valid measurements. - Accuracy: this refers to how closely the measured values agree with the true or correct value. - Precision: this refers to how closely the measurements agree with each other.

ANALYZING DATA: BMI The concepts of accuracy and precision will be demonstrated by comparing three different methods used to track a person’s percent body fat. Percent Body Fat: weight of the person’s fat/ person’s total body weight The most common methods used to estimate the fat content of the individual 1- Body Mass Index (BMI) BMI = mass (kg)/ height (m)2 2- Measuring the thickness of the subcutaneous fat layer using skinfold calipers. 3- Bioelectrical impedance analysis (BIA)

ANALYZING DATA: BMI VS EXERCISE PULSE Using excel, graph the exercise pulse of each Biology 2425 student versus his/her BMI.