Descriptive Statistics (2–3 pages)
The researchers investigating energy drink consumption and alcohol use want to know a bit more about how much caffeine is consumed by participants. The following dataset contains 30 participants’ caffeine consumption for a week, measured in milligrams.
270, 761, 707, 908, 891, 842, 866, 925, 305, 614, 890, 744, 599, 668, 383, 476, 922, 577, 477, 922, 617, 850, 260, 706, 270, 532, 922, 395, 683, 86
Submit calculations of the following measures of central tendency and measures of variability by hand. Write your responses in your own words. It is acceptable to number your answers, but do not copy and paste the questions into your answer document.
Note: Be sure to fully explain how you arrived at your answers and support your responses with evidence from the text and Learning Resources.
1. Compute and interpret the following hand-computed statistics for the given scenario. For each measure you compute by hand, include an explanation of your calculations (explain the steps) and what that measure tells you about the caffeine consumption of the sample. For example, each of your answers might look something like this:
“The mean of this sample is ______ milligrams of caffeine consumed in a week.The mean is calculated by _________________.The mean tells me that participants in the sample consumed ____________ in the first week.”
e. Deviation of the highest score from the mean
f. Estimated population standard deviation
2. Compute the following statistics for the given scenario:
a. ∑X2. (The sum of the squared Xs). Explain your calculations, but you do not need to interpret this result in relation to the scenario.
b. (∑X)2. (The squared sum of X). Explain your calculations, but you do not need to interpret this result in relation to the scenario.
c. Compute the mean in SPSS and report them in your answer document. Note: Your hand-calculated mean and standard deviation may differ somewhat from the calculations in SPSS due to rounding.
d. Compute the standard deviation in SPSS and report them in your answer document. Note: Your hand-calculated mean and standard deviation may differ somewhat from the calculations in SPSS due to rounding.
3. Answer the following questions about the data:
a. Identify the type of distribution (positive skew, negative skew, or normal distribution) the data create. Explain how you know the type of distribution and what it tells you about the sample.
b. Without redoing any calculations, think critically about how each measure would be affected if the lowest score was eliminated from the dataset. Explain if each measure (mean, median, mode, deviation of the highest score from the mean, and standard deviation) would increase, decrease, or stay the same.