Standard deviation (Higher tier)：練習問題

A distribution of test scores has a mean of 65, a median of 72, and a mode of 80. Based on these measures of central tendency, what is the skewness of the distribution?

For a data set where the Lower Quartile (LQ) is 15 and the Upper Quartile (UQ) is 35, an outlier is defined as any value more than \(1.5 \times \text{IQR}\) above the UQ or below the LQ. Which of the following values would be considered a large outlier?

A set of data is displayed in a stem and leaf diagram. The leaf values for one stem are 2, 5, 5, 8, 9. What is the median of this specific row if the stem represents tens and the leaves represent units?

A histogram is drawn for grouped data with unequal class widths. The class \(10 < x \le 20\) has a frequency of 50. The class \(20 < x \le 50\) has a frequency of 60. What is the ratio of the frequency density of the first class to the frequency density of the second class?

A data set consists of the following values:
7, 12, 15, 18, 45.
Identify the outlier in this data set and suggest one reason why it might have occurred in the context of data cleaning.<\/p>

A distribution of test scores has a mean of 62, a median of 55, and a mode of 48.
Determine the skewness<\/b> of this distribution and explain what this tells you about the spread of the data relative to the median.<\/p>

A health clinic tracks the recovery time (in days) of patients after a specific treatment. The data for 10 patients is shown below: