# 2142b Univariate Data - Box & Whisker Summary

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Anthony Nunan
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Data Set B
72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83,
77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70

• 1.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 How many students took part?

Explanation
Count the number of items in the data set.

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• 2.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 What is the median scored for the test?

Explanation
Find the middle value ... remember, find n, then add 1 ... and divide by 2. That will tell you which term is the middle term. The middle term is the median. If n is an odd number, then the median may fall between two numbers. Just find the average of those two numbers.

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• 3.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 What is the range for this data set?

Explanation
Range = maximum number - minimum number

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• 4.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 What is the interquartile range for this data set?

Explanation
Interquartile range (IQR) = Q3 - Q1

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• 5.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 What is the value for Q1 for this data set?

Explanation
The value for Q1 represents the first quartile of the data set. In order to find Q1, we need to arrange the data in ascending order. Once the data is sorted, we can find the position of Q1 by multiplying the total number of data points (in this case, 23) by 0.25. This gives us a position of 5.75. Since this is not a whole number, we can take the average of the values in the 5th and 6th positions, which are both 72. Therefore, the value for Q1 in this data set is 72.

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• 6.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 What was the lowest mark?

Explanation
The lowest mark in the recent geography test was 65. This can be determined by finding the smallest number among the given percentages, which is 65.

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• 7.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 What was the highest score?

Explanation
The highest score in the geography test was 96. This can be determined by looking at the list of percentages and identifying the highest number, which in this case is 96.

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• 8.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 Are there any outliers in this data set?

Explanation
In statistics, outliers are data points that significantly differ from the majority of the data set. To determine if there are any outliers, we can use methods such as the interquartile range (IQR) or z-scores. However, without any additional information or specific criteria for what constitutes an outlier in this context, it is difficult to definitively identify any outliers in the given data set. Therefore, the answer is "No".

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• 9.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 To detect if there are any outliers, we need to define our fences. What is the upper fence for this data?

Explanation
multiply the IQR by 1.5 and then add it to Q3

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• 10.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 What is the value for Q3 range for this data set?

Explanation
Find the middle of the upper half. Same technique as finding the median.

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• 11.

### The following percentages were received in a recent geography test. 72, 67, 68, 72, 78, 83, 86, 75, 65, 77, 96, 83, 77, 84, 89, 89, 76, 81, 87, 67, 91, 77, 70 To detect if there are any outliers, we need to define our fences. What is the lower fence for this data?

Explanation
multiply the IQR by 1.5 and subtract it from Q1

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• Current Version
• Mar 20, 2023
Quiz Edited by
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• Oct 25, 2013
Quiz Created by
Anthony Nunan

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