Analyze data from experiments

Experimental data are organized in tables, dot plots, histograms, or box plots and interpreted as distributions, with attention to the number of observations, typical value (mean or median), variability (range, interquartile range, or mean absolute deviation), and unusual results. Comparisons between experimental conditions require considering both center and spread; a difference in sample results may reflect natural variation rather than a definitive conclusion. Formal statistical inference, sampling distributions, hypothesis tests, and confidence intervals are not included.

Detailed Explanation: Analyze data from experiments

When you analyze experimental data, look for four things:

Number of observations: How many results were recorded?
Typical value: What result is usual? Use the mean or median.
Variability: How much do the results differ? Use the range or another measure of spread.
Unusual results: Is any value much higher or lower than the others?

When comparing two experimental conditions, compare both the center and the spread. A difference in the results does not always prove that one condition is better because natural variation can occur.

Example

Students tested how far paper airplanes flew under two conditions.

Condition A (meters)	Condition B (meters)
8	7
9	8
9	10
10	11
10	12
12	16

Step 1: Count the observations

There are $6$ airplane flights for Condition A and $6$ for Condition B.

Step 2: Find the typical value

The data are already in order. Since there are $6$ values, the median is the mean of the middle two values.

For Condition A, the middle values are $9$ and $10$ :

\text{Median}=\frac{9+10}{2}=9.5

For Condition B, the middle values are $10$ and $11$ :

\text{Median}=\frac{10+11}{2}=10.5

The typical flight for Condition B was $1$ meter farther.

Step 3: Find the spread

Use the range:

\text{Range}=\text{greatest value}-\text{least value}

For Condition A:

12-8=4\text{ meters}

For Condition B:

16-7=9\text{ meters}

Condition B has a larger range, so its results were more spread out and less consistent.

Step 4: Look for unusual results

The value of $16$ meters in Condition B is much farther than most of the other Condition B results, which are between $7$ and $12$ meters. It may be an unusual result.

Step 5: State what the data show

Condition B had a slightly higher typical distance: its median was $10.5$ meters compared with $9.5$ meters for Condition A. However, Condition B also had more variability, with a range of $9$ meters compared with $4$ meters. Therefore, Condition B may have helped the airplanes fly farther, but the results are not consistent enough to say that it always works better. Some of the difference could be due to natural variation in the flights.

Learn by doing: Analyze data from experiments

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Statistics - Quartiles - Data Set (With Outliers) to Box Plot

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