# Measures of Central Tendency

Refer to the below data sets of scores, X, Y and Z, from two 5-point quizzes to answer the questions.

X f Y f Z f

5 4 5 1 5 0

4 3 4 2 4 0

3 0 3 4 3 1

2 1 2 1 2 4

1 1 1 1 1 1

0 1 0 1 0 4

#1. (a-c) Compute the mean for each set of scores.

#2. (a-c) Compute the median for each set of scores.

#3. (a-c) Compute the mode for each set of scores. (d) Which data set is multimodal, that is, it has more than one modes?

#4. (a) What is a positively skewed distribution? (b) What measure of central tendency would be used with this type of distribution? (c) Why?

#5. (a) What is a negatively skewed distribution? (b) What measure of central tendency would be used with this type of distribution? (c) Why?

#6. (a) What is a symmetric distribution? (b) What measure of central tendency would be used with this type of distribution? (c) Why?

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Chapter 4 Exercises

Instructions: Complete the work below, making any necessary computations on separate sheets of paper, and then use the Chapter 4 Exercise Form to record your answers.

Refer to the below data sets of scores, X, Y and Z, from two 5-point quizzes to answer the questions.

X f Y f Z f

5 4 5 1 5 0

4 3 4 2 4 0

3 0 3 4 3 1

2 1 2 1 2 4

1 1 1 1 1 1

0 1 0 1 0 4

#1. (a-c) Compute the mean for each set of scores.

The mean is the average of all the numbers. You calculate it by adding all the numbers together and dividing by the number of observations. When you have a table like this, showing the frequencies (f) for each value (x, y, or z), you can calculate the mean by writing out all the numbers and calculating the mean as above, or by multiplying each value by its respective frequency, adding them together, then dividing by the total. Both methods are shown below; the means are in ...