Quiz On Range, Interquartile And Semi-interquartile Range

Explanation
The range is the difference between the highest and lowest values in a set of numbers. In this case, the highest mark Ann got was 10 and the lowest mark was 3. Therefore, the range of the marks is 10 - 3 = 7.

Explanation
The range is a measure of dispersion that calculates the difference between the largest and smallest values in a given set of data. It provides information about the spread or variability of the data. By finding the range, we can determine the extent to which the values deviate from each other. In contrast, the mean, median, and mode are measures of central tendency that provide information about the average or most representative value in the data set.

Explanation
The interquartile range is the correct answer because it is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1). It is used to measure the spread or dispersion of a dataset and is particularly useful when there are outliers present. By subtracting Q1 from Q3, we can determine the range within which the middle 50% of the data falls, providing a more robust measure of variability compared to the regular range.

Explanation
The interquartile range is a measure of the spread of a dataset. It is calculated by finding the difference between the first quartile (Q1) and the third quartile (Q3). In this case, the dataset is {5, 7, 5, 4, 7, 6, 8, 9, 9, 8, 7, 5, 6, 10, 10, 9, 5, 10}. When the dataset is sorted in ascending order, we have {4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10}. The first quartile is the median of the lower half of the dataset, which is 6. The third quartile is the median of the upper half of the dataset, which is 9. Therefore, the interquartile range is 9 - 6 = 3.

Explanation
The semi interquartile range is a measure of the spread of data. It is calculated by finding the difference between the upper quartile (Q3) and the lower quartile (Q1) and then dividing it by 2. In this case, the lower quartile is 159 cm (the average of the two middle values) and the upper quartile is 164 cm (the average of the two middle values). The difference between these two values is 5 cm, and dividing it by 2 gives us 2.5 cm. Therefore, the semi interquartile range is 2.5 cm.

Explanation
The interquartile range is a measure of variability that represents the range of the middle 50% of the data. To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3). In this case, the first quartile is 6 and the third quartile is 8. The interquartile range is then calculated by subtracting Q1 from Q3: 8 - 6 = 2. Therefore, the correct answer is 2.

Explanation
The given set of scores is 5, 6, 3, 2, and 1. To find the median, we need to arrange the scores in ascending order. When we do that, the sequence becomes 1, 2, 3, 5, 6. The median is the middle value in the sequence, which is 3.

Explanation
The semi-interquartile range is a measure of the spread or dispersion of a dataset. It is calculated by finding the difference between the first quartile (Q1) and the third quartile (Q3), and then dividing that difference by 2. In this case, the first quartile is 2 and the third quartile is 4. The difference between them is 2, and dividing that by 2 gives us 1. Therefore, the semi-interquartile range is 1.25.

Explanation
The median score is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are already in order from smallest to largest. Since there are an even number of scores (4), the median is the average of the two middle numbers. The two middle numbers are 3.5 and 4.5, so the median score is 3.5.

Explanation
The median is the middle value in a set of data when the data is arranged in ascending or descending order. In this case, the heights are already arranged in ascending order. The middle value is 75 cm, which is the third value in the set. Therefore, the median height of the children from the table is 75 cm.