Statistics Refresher Course

Which of the following graphs is most appropriate for displaying the distribution of a single quantitative variable?

• Pie chart

• Bar graph

• Histogram

• Pareto chart

Answer explanation

Histogram

Explanation: A histogram is specifically used to display the distribution of quantitative data by grouping data into intervals.

A histogram for a dataset is heavily skewed to the right. Which of the following is likely true about the relationship between the mean and median?

• Mean < Median

• Mean = Median

• Mean > Median

• Mean is undefined

Answer explanation

Answer: Mean > Median
Explanation: In a right-skewed distribution, the mean is pulled in the direction of the skew, making it greater than the median.

A company wants to compare the number of customer complaints received in four different regions. Which graph is most suitable?

• Histogram

• Bar chart

• Dot plot

• Stem-and-leaf plot

Answer explanation

Answer: Bar chart
Explanation: Bar charts are ideal for comparing categorical data, such as regions.

Which of the following statements best distinguishes a histogram from a bar chart?

• A histogram can only show categorical data.

• A bar chart uses intervals while a histogram does not.

• Bars in a histogram are separated while bars in a bar chart are touching.

• Bars in a histogram touch, indicating a continuous scale.

Answer explanation

Answer: Bars in a histogram touch, indicating a continuous scale.

Explanation: In histograms, adjacent bars touch to represent continuous intervals; in bar charts, bars are separated to show distinct categories.

Given the following stem-and-leaf plot:

What is the median of the dataset?

• 55

• 50

• 52.5

• 53.5

Answer explanation

Answer: 52.5
Explanation: The ordered data: 41, 43, 47, 50, 55, 59, 62, 68. The median is the average of the 4th and 5th values: (50+55)/2 = 52.5 → rounded or represented as 52 if using midpoint conventions.

A pie chart shows five categories of expenses. If one category represents 90° of the circle, what percent of the total does it represent?

• 15%

• 25%

• 50%

• 90%

Answer explanation

Answer: 25%
Explanation: A circle is 360°. 90°/360° = 0.25 = 25%.

What is the mean of the following data set: 4, 8, 6, 10, 12?

• 6

• 8

• 10

• 12

Answer explanation

Answer: 8
Explanation: Mean = (4+8+6+10+12)/5 = 40/5 = 8.

Which of the following statements is true about the standard deviation?

• It can be negative.

• It is resistant to outliers.

• It measures the average distance from the median.

• It increases when there is more variability in the data.

Answer explanation

Answer: It increases when there is more variability in the data.
Explanation: Standard deviation reflects the spread of data around the mean. More variability leads to a larger standard deviation.

A company wants to compare employee salaries across departments. Which measure of center is most appropriate if some departments have outlier salaries (e.g., top executives)?

• Mean

• Mode

• Median

• Range

Answer explanation

Answer: Median
Explanation: The median is more resistant to outliers and skewed data than the mean.

The five-number summary of a dataset is:
Minimum = 12, Q1 = 18, Median = 22, Q3 = 30, Maximum = 45
What is the interquartile range (IQR)?

• 17

• 15

• 22

• 12

Answer explanation

Answer: 12
Explanation: IQR = Q3 – Q1 = 30 – 18 = 12.