Chapter 4

Question 1

What are the three important characteristics of distributions?

Answer 1

Shape, centre. width.

Question 2

Central tendency

Answer 2

The middle of the distribution.

Question 3

Mode

Answer 3

The most frequently occurring value in a distribution. It is a measure of central tendency appropriate for any variable (nominal, ordinal, interval/ratio).

Question 4

What are the three measures of central tendency?

Answer 4

Mode, median, mean.

Question 5

How do you eyeball-estimating the mode?

Answer 5

The mode is the value of the variable on the X-axis not the highest point on the curve. The highest point of the curve represents the frequency of the mode, not the mode itself.

Question 6

How can you determine the mode of ordinal or interval ratio data?

Answer 6

1. Note the highest frequency that occurs in the frequency distribution.
2. Note the highest frequency in a frequency distribution that uses class intervals.
   The results of either option are not identical.

Question 7

Median

Answer 7

The value that is the midpoint of a data set. It is a measure of central tendency appropriate for ordinal or interval/ratio variables. e.g. the value for which half the entries in the data set are larger and half are smaller.

Question 8

What types of data can the median be used for?

Answer 8

Ordinal and interval/ratio data because “larger” and “smaller” do not apply to nominal variables.

Question 9

How can you eyeball estimate the median from a frequency distribution?

Answer 9

Find the point on the distribution which divides the area under the distributions into halves.

Question 10

How do you compute the median?

Answer 10

1. Put all the entries in the data set in order from largest to smallest. There should be the same number of items in the list as there are entries in the original data set. e.g. If one value has frequency 3, for example, it should appear three times in the list.
2. Determine whether the data set has an odd number or an even number of entries (whether n is an odd or even number).
3. If n is an odd number, the median is the middle point in the ordered data. The position for the midpoint is given by (n + 1)/2.
4. If n is an even number, then there is no middle point, and the median is half-way between the two points closes to the middle. Take these two numbers closest to the middle, add them together and divide by 2 (? + ?)/2 = median

Question 11

Mean

Answer 11

The sum of all values of a variable divided by the number of values. It is a measure of central tendency appropriate for interval/ratio variables.