Box & Whisker Quiz

The five-number summary provides a concise description of the distribution of the data set. It includes the minimum value (65), the first quartile (Q1) or the value below which 25% of the data falls (72), the median (77) or the value below which 50% of the data falls, the third quartile (Q3) or the value below which 75% of the data falls (86), and the maximum value (96). In this case, the five-number summary is 65, 72, 77, 86, 96.

The size of the distribution for this data is 17. This is because there are 17 members of the hockey club who completed the walkathon, as indicated in the question.

The size of this distribution is determined by counting the number of data points in the given set. In this case, there are 23 data points, which corresponds to the size of the distribution.

The value of 'n' for this distribution is 30. This can be determined by looking at the box and whisker plot, which shows the median as the line inside the box. In this case, the line is positioned at the 30 mark on the number line, indicating that the median value is 30. Therefore, 'n' is equal to 30.

The middle fifty percent of the cyclists have a resting heart rate between 72 and 86. This means that half of the recorded heart rates fall below 72 and the other half fall above 86. Therefore, the range of heart rates for the middle fifty percent is between 72 and 86.

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The value of 'n' in this distribution refers to the total number of data points or observations. In this case, the given data set contains 13 values, so the value of 'n' is 13.

The range for a data set is the difference between the largest and smallest values. In this case, the largest value is 18 and the smallest value is 8. Therefore, the range is 18 - 8 = 10 years.

Battery B had the worst result.

The interquartile range is a measure of the spread of data that represents the range between the first quartile (Q1) and the third quartile (Q3). To find the interquartile range, we first need to arrange the ages in ascending order: 8, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 18, 18. The first quartile (Q1) is the median of the lower half of the data, which is 14. The third quartile (Q3) is the median of the upper half of the data, which is 17. Therefore, the interquartile range is 17 - 14 = 3 years.

The question asks about the battery with the longest life on average. The correct answer is "Battery B" because it is stated in the question that two types of batteries were tested in a remote control helicopter. Since Battery B is mentioned separately from the other battery, it can be inferred that Battery B had the longest life on average compared to the other battery.

Battery B is the most consistent because it consistently provided better performance compared to the other battery during the testing of the remote control helicopter.

The worst time that any battery lasted, as shown by the parallel box plots, is 13 minutes. This means that at least one battery lasted for only 13 minutes before running out of power.

The interquartile range (IQR) is a measure of the spread of data in a box plot. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). In this case, the IQR of battery A is 6 minutes, which means that the middle 50% of the data falls within a range of 6 minutes.

The statement "The distribution size for Battery B was 18 minutes" is incorrect because the distribution size refers to the range of values in a dataset, not a specific value.

The box and whisker plot shows that the distribution of ages is approximately symmetrical, as the median line is in the middle of the box and the whiskers are of similar length. However, there is an outlier present, which is a data point that is significantly different from the rest of the data. Therefore, the best description for the shape of this distribution is approximately symmetrical with an outlier.

The box plot shows that the majority of the times are clustered towards the higher end of the scale, with a few outliers on the lower end. This indicates that the distribution is negatively skewed, meaning that the tail of the distribution is stretched towards the lower values. The presence of the outlier further supports the fact that the distribution is negatively skewed.

The interquartile range is a measure of the spread of the middle 50% of the data. In this case, the interquartile range is 4 years, which means that the ages of the middle 50% of the soccer club members are spread out over a range of 4 years.

The range for this data set is 11 years. The box and whisker plot shows the minimum and maximum ages of the members of the junior soccer club. The minimum age is 11 years and the maximum age is also 11 years, resulting in a range of 11 years.

The size of the distribution of Battery B is 24. This means that there were 24 batteries of type B tested in the remote control helicopter.

The median is the middle value in a set of data when the data is arranged in ascending order. In this case, the data set is already given, so we can find the median by arranging the numbers in ascending order: 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6. The middle value is 2, so the median for this data set is 2 bikes.

The box plot shows that the distribution is negatively skewed, meaning that the tail of the distribution is longer on the left side. This indicates that the majority of the swimmers took less time to complete the lap, with a few outliers taking significantly longer.

The box plot shows that the majority of the data is concentrated towards the lower end of the distribution, with a long tail extending towards the higher end. This indicates a positively skewed distribution. Additionally, there is an outlier present, as indicated by the dot outside of the whiskers. Therefore, the best description for the shape of this distribution is positively skewed with an outlier.

The range for a data set is the difference between the maximum and minimum values. In this case, the maximum value is 6 and the minimum value is 1. Therefore, the range is 6 - 1 = 5 bikes.

The upper fence for calculating outliers in this data set is 7 bikes. The upper fence is calculated by adding 1.5 times the interquartile range (IQR) to the third quartile (Q3). In this case, the third quartile is 4 and the IQR is 2. Therefore, 1.5 times the IQR is 3 and adding that to Q3 gives us 7. This means that any value above 7 can be considered an outlier in this data set.

The range for this data set is 31 bpm. The range is calculated by subtracting the smallest value from the largest value in the data set. In this case, the smallest value is 65 bpm and the largest value is 96 bpm. Therefore, the range is 96 - 65 = 31 bpm.

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The median is the middle value of a data set when it is arranged in ascending order. In this case, the box and whisker plot does not provide the exact values of the data set, but we can estimate that the median is closest to the value represented by the line in the middle of the box. Based on the given answer choices, 15.5 years is the closest option to the estimated median.

The range for this data set is 11 years. The range is calculated by subtracting the minimum value from the maximum value in the data set. In this case, the minimum age is 11 years and the maximum age is also 11 years, so the difference between them is 0. However, since the range is defined as the difference between the maximum and minimum values, we can say that the range is 11 years.

The five-number summary for this data set is 8, 13.5, 15.5, 17.5, and 18. The first number, 8, represents the minimum age in the data set. The second number, 13.5, represents the lower quartile or the median of the lower half of the data. The third number, 15.5, represents the median of the entire data set. The fourth number, 17.5, represents the upper quartile or the median of the upper half of the data. Finally, the fifth number, 18, represents the maximum age in the data set.

The lower fence for calculating an outlier is closest to 7.5 years. In a box and whisker plot, the lower fence is calculated by subtracting 1.5 times the interquartile range (IQR) from the first quartile (Q1). The IQR is the range between the first quartile and the third quartile. In this case, since the lower whisker extends to the first quartile, the lower fence is equal to Q1. Based on the given information, the lower fence is closest to 7.5 years.

The correct answer is 72 bpm. This is because 25% of the recorded resting heart rates are less than or equal to 72 bpm.

The value of 'n' in this distribution refers to the total number of data points or observations in the dataset. In this case, the resting heart rates of the group of cyclists are recorded 11 times, indicating that there are 11 data points in the distribution.

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The shape of the distribution of the data set is described as negatively skewed because the tail of the plot is longer on the left side and the majority of the data is concentrated on the right side. This indicates that there are more members of the tae kwon do class who are younger, resulting in a skew towards the younger ages.

The five number summary for a data set includes the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. In this case, the minimum value is 1, the first quartile is 2, the median is also 2, the third quartile is 4, and the maximum value is 6. Therefore, the five number summary for this data set is 1, 2, 2, 4, 6.

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