1. Data Analysis-Descriptive Statistics
Biotechnology I

2. Essential Question
How do scientists summarize and interpret their data?

3. Think-Pair-Share???
You are examining the effect of fertilizer on the growth of corn plants. In one experimental treatment (+ fertilizer), the height of the corn plants were 10 cm, 15 cm, 20 cm, 6 cm, and 25 cm.
Explain why the differences in height even though plants received the same experimental treatment.

4. Purpose of Statistics
Individual variation and uncertainty present in natural world
Interpretation of data
must distinguish between biological effect and effect by chance
Accomplished through statistics

5. Descriptive Statistics
Used for organizing, summarizing and describing data
Shows variation in the data
Example: deviation from the mean

6. Key Terms
Population- entire group of events, objects, results, or individuals which share unifying characteristic
Variable- characteristics of the population that can be measured
Sample-selected group that is representative of the population

7. Measurement of Central Tendency
Mode-value that occurs with highest frequency
Mean- sum of values divided by the number of values
Median-middle value of a data set
A number halfway between highest and lowest value, when arranged in ascending order
Odd number of values
Median middle value in the sequence
Even number of values,
median average of the two middle numbers

8. Sample Problem
Suppose you are investigating the height of high school students. You measure the height of every student in your classes and obtain the following data:
Height (cm) 175, 181, 160, 189, 172, 160, 167, 163, 161, 179, 160
Calculate the mode, mean, and the median for these measurements.

9. Answer to Sample Problem
Mode=160
Mean = / 10 =
Median = ( ) /2 =

10. Measure of Dispersion Range – measures the spread of the data;
Indicates the highest and lowest point in the data set

11. Standard Deviation Indicates spread in the data set
Variance = how far each of the data points deviates from the mean
s2 = (S(xi - x )2) / n
Standard deviation = Square root of variance = s;

12. Outliers Data point(s) that lie outside the other data points Reasons
Result from experimental errors. Examples:
Improperly removing and preparing a sample
Malfunctioning instrument
Inattentativeness of lab technician OR
May be significant experimental event that needs further investigating

13. Quality Control Department
Responsible for monitoring processes during production and performing laboratory tests on final product to ensure product meets company standards
What happens when tests show product doesn’t meet expected standard?
Question asked: Is that normal variability or is there a problem in the process?
Normally, company knows the amount of variability inherent to production process
If outlier outside a mean + 2 SD suggests there is a problem

14. Standard Error
Indicates how well sample mean matches up with population mean
SE = s/SQR of n
s = standard deviation
SQR = square root
n = sample size
Commonly used as error bars in graphical display

15. 95% Confidence Interval
Certainty the range of values within the interval contains the population mean
Typically, error bars on graphical displays are + 2 SE
Represents 95% confidence interval

16. Comparison of Error Bars between Two Experimental Groups
If error bars overlap – not significantly different
If error bars do not overlap – significantly different
Further statistical tests warranted

17. Answer the following questions in your IAN
Explain the difference between mode, mean and median.
Explain what range and variance in a data set represents.
Why do companies have a quality control division?
How do companies know they have a problem in production?
What do error bars represent?
What do error bars tell an investigator about similarity or differences between two experimental groups?