Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityHard
A botanist is studying the heights (in cm) of a particular species of plant. The observed heights are: 22, 25, 20, 28, 23, 26, 21. What is the standard deviation of these plant heights, rounded to two decimal places?
- A3.52
- B3.19
- C2.96
- D3.31
Show answer & explanationAnswer & explanation
Correct answer: C. 2.96
First, calculate the mean: (22+25+20+28+23+26+21)/7 = 165/7 ≈ 23.57. Next, calculate the variance by finding the squared difference of each value from the mean, summing them, and dividing by (n-1) for a sample or n for a population. Assuming this is a sample, variance = ( (22-23.57)^2 + (25-23.57)^2 + ... + (21-23.57)^2 ) / (7-1) ≈ 8.76. The standard deviation is the square root of the variance: sqrt(8.76) ≈ 2.96.
Why the other options are wrong
- A. This value is incorrect and likely results from a calculation error.
- B. This value would be obtained if there was an error in calculating the mean or the sum of squared differences.
- D. This value would be obtained if there was an error in calculating the mean or the sum of squared differences.
Standard Deviation
A measure of the amount of variation or dispersion of a set of values, indicating how spread out the numbers are from the mean.
- Square root of the variance.
- Expressed in the same units as the data.
- A low standard deviation means values are close to the mean; high means spread out.
Memory trick: Dispersion: spread out, how far from the mean.