Calculate the 5-number summary of the skewed dataset 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 29. When constructing the box plot on a number line, which explains a reason why the dataset is skewed?
The 5 numbers in the summary are equally spread apart.
The median is exactly in the middle of the box.
The right whisker is much longer than the left whisker.
The whiskers are the same length.
The 5-number summary of the dataset is:
Minimum: 15
Q1 (first quartile): 16.5
Median: 18
Q3 (third quartile): 19
Maximum: 29
When constructing the box plot on a number line, one reason why the dataset is skewed is because the right whisker is much longer than the left whisker. This indicates that there are some outliers on the higher end of the dataset, causing it to be skewed to the right.
Calculate the 5-number summary of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16. Which of the following choices is quartile 3?
9
2.5
8
6.5
To find the 5-number summary of the dataset provided:
Arrange the dataset in ascending order: 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16
Minimum: 5
Q1 (first quartile): (6+6)/2 = 6
Median: (8+8)/2 = 8
Q3 (third quartile): (9+9)/2 = 9
Maximum: 16
So, the third quartile (Q3) is 9, which matches with the option "9".
Which option is true about the outliers of the skewed dataset 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 14, 16?
The outliers of the dataset are 14 and 16.
There are no outliers in the dataset.
The only outlier of the dataset is 16.
The outliers of the dataset are 5, 14, and 16.
To determine the outliers in a dataset, one common method is to use the interquartile range (IQR) method.
First, calculate the IQR:
IQR = Q3 - Q1
For the given dataset:
Q1 = 6
Q3 = 9
IQR = 9 - 6 = 3
Next, calculate the lower bound and upper bound for outliers:
Lower bound = Q1 - 1.5 * IQR
Upper bound = Q3 + 1.5 * IQR
Lower bound = 6 - 1.5 * 3 = 1.5
Upper bound = 9 + 1.5 * 3 = 13.5
Any values in the dataset that are below the lower bound or above the upper bound are considered outliers.
In the dataset:
- 5, 14, and 16 are outside the calculated bounds: 5 is below the lower bound, and 14 and 16 are above the upper bound.
Therefore, the outliers of the dataset are 5, 14, and 16.
The option "The outliers of the dataset are 5, 14, and 16" is true.
A stock analyst is comparing the interquartile range of the day’s stock prices of Stock A and Stock B. Stock A has an interquartile range of 3, and Stock B has an interquartile range of 11. What interpretation can be made from the interquartile range of each stock?
The price of Stock B is higher than the price of Stock A by 7.
The stock price for Stock B is higher than the price for Stock A.
Stock B has more variability than Stock A.
Stock A has more variability than Stock B.
The interquartile range (IQR) measures the spread and variability of a dataset, specifically the middle 50% of the data.
In this case:
- Stock A has an IQR of 3
- Stock B has an IQR of 11
The IQR is a measure of variability within the middle 50% of the data. A larger IQR indicates that there is more variability in that range of the data.
Based on the given information, Stock B has a larger IQR of 11 compared to Stock A's IQR of 3. This means that Stock B has more variability in its stock prices compared to Stock A.
Therefore, the correct interpretation is: Stock B has more variability than Stock A.