Question

question 26
if a set of scores for a variable is displayed in a frequency distribution polygon, which scale of measurement was used to measure the variable?
nominal or ordinal
ordinal or interval
ratio or ordinal
interval or ratio

question 27
a set of scores ranges from a high of x = 18 to a low of x = 5. if these scores were put in a grouped frequency distribution table with an interval width of 2 points, which of the following would be the top interval in the table?
4 - 5
5 - 6
18 - 19
17 - 18

question 28
a sample of scores has a mean of m = 26, a median of 28, and a mode of 29. what is the most likely shape for the sample distribution?

Explanation:

Question 26

Step1: Recall scale - type for frequency polygon

Frequency - distribution polygons are used for interval or ratio - scaled data. Nominal and ordinal data are not appropriate for this graphical representation as they do not have a meaningful order or numerical value for the operations involved in creating a frequency - distribution polygon.

Question 27

Step1: Determine top interval

The highest score is \(X = 18\). With an interval width of 2 points, the top interval should start at 18. The interval notation for a grouped frequency distribution with an upper - limit of 18 and width 2 is \(18 - 19\).

Question 28

Step1: Analyze relationship between mean, median, and mode

When the mean \(M=26\), median \(= 28\), and mode \(=29\), the mean is less than the median which is less than the mode. This indicates a negatively skewed distribution. In a negatively skewed distribution, the tail of the distribution is pulled towards the lower values, causing the mean to be pulled in the direction of the tail and be less than the median and mode.

Answer:

Question 26: interval or ratio
Question 27: 18 - 19
Question 28: Negatively skewed