Q: Which formula is used to determine the lower fence for identifying outliers in a boxplot?

$\text{Lower Fence} = Q_1 - 1.5 \times IQR$

Question 1

Which of the following best describes the purpose of a boxplot in statistics?

Accepted Answer

To display the distribution of a dataset, highlighting the median, quartiles, and potential outliers.

Question 2

Given the dataset: 56, 67, 68, 72, 74, 75, 88, 90, 97, 99, what is the median value?

Accepted Answer

$\frac{74 + 75}{2} = 74.5$

Question 3

In a boxplot, what do the 'whiskers' represent?

Accepted Answer

They extend to the smallest and largest non-outlier values in the dataset.

Question 4

How is the interquartile range (IQR) calculated from a dataset?

Accepted Answer

$IQR = Q_3 - Q_1$

Question 5

Which formula is used to determine the lower fence for identifying outliers in a boxplot?

Accepted Answer

$	ext{Lower Fence} = Q_1 - 1.5 	imes IQR$

Question 6

A dataset has $Q_1 = 6$, $Q_3 = 9$, and $IQR = 3$. What is the upper fence for outlier detection?

Accepted Answer

$9 + 1.5 	imes 3 = 13.5$

Question 7

If a value in a dataset is greater than the upper fence, how is it represented in a boxplot?

Accepted Answer

As an individual point, marked as an outlier.

Question 8

Which of the following steps is NOT required when creating a boxplot in StatCrunch?

Accepted Answer

Calculating the mean of the dataset.

Question 9

Why might the quartile values in StatCrunch differ slightly from hand calculations?

Accepted Answer

StatCrunch uses a specific quartile convention that may differ from manual methods.

Question 10

Given the dataset 2, 4, 5, 6, 7, 8, 9, 10, 30, which value is identified as an outlier using the boxplot method?

Accepted Answer

$30$

Question 11

If you want to display a horizontal boxplot in StatCrunch, which option should you select?

Accepted Answer

Check the 'Draw boxes horizontally' option.

Question 12

Which of the following is a correct interpretation of the line inside the box in a boxplot?

Accepted Answer

It represents the median (Q2) of the dataset.

Question 13

A business analyst uses a boxplot to compare sales data from two regions. Region A's boxplot is much wider than Region B's. What does this indicate?

Accepted Answer

Region A has greater variability in sales than Region B.

Question 14

Which of the following best explains why outliers are important to identify in business data analysis?

Accepted Answer

Outliers can indicate errors, unusual events, or important business insights.

Question 15

If the minimum value in a dataset is below the lower fence, how will it appear in the boxplot?

Accepted Answer

It will be shown as an individual point, indicating an outlier.

Question 16

Which step should you take if you want to change the data column used in a boxplot after generating it in StatCrunch?

Accepted Answer

Click Options > Edit, then select a new data column.

Question 17

A company’s boxplot of monthly profits shows a median line closer to the lower quartile (Q1) than the upper quartile (Q3). What does this suggest about the distribution of profits?

Accepted Answer

The distribution is skewed to the right (positively skewed).

Boxplot Construction and Interpretation Using StatCrunch

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