You are being asked to compute and interpret several measures of central tendency and measures of variability, both by hand and with SPSS.Be sure to fully explain the rationale for your answer to each question, including evidence from the text and learning resources. Between 3 and 5 sentences per question should allow you to provide sufficient answers, and explanations.

SCENARIO:

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.

842, 110, 315, 908, 599, 890, 476, 771, 706, 529, 383, 683, 722, 850, 891, 668, 925, 395, 919, 919, 910, 577, 310, 270, 635, 707, 895, 477, 260, 614

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

What ive computed already:

The mean of this sample is 638.5 milligrams of caffeine consumed in a week

The median of this sample is 675.5

The mode of this sample is 919

The range of the sample is 815

The deviation of the highest score from the mean is 286.5

The population standard deviation in this sample is 235.7

1.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.

2.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.