Please help
Calculate the interquartile range of the following data.
{35,20,41,47,79,83,83,97,120}
Q1=
Q2=
IQR=
Values lower than blank and higher than blank are considered outliers.
The outlier in this data set is blank
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3).
1. Arrange the data in ascending order: {20, 35, 41, 47, 79, 83, 83, 97, 120}
2. Find the median (Q2) of the data set. Since there are an odd number of data points, the median is the middle number, which is 79.
3. Find the median of the lower half of the data to get Q1. The lower half is {20, 35, 41, 47}. The median of this set is (35+41)/2 = 38.
4. Find the median of the upper half of the data to get Q3. The upper half is {83, 83, 97, 120}. The median of this set is (83+97)/2 = 90.
5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 90 - 38 = 52.
So, Q1 = 38, Q3 = 90, and IQR = 52.
Values lower than 38 - 1.5*52 = -53 and higher than 90 + 1.5*52 = 166 are considered outliers.
There are no outliers in this data set.
Where do you get the 1.5 please?
The value of 1.5 is a commonly used multiplier in identifying outliers using the interquartile range (IQR) method. This multiplier is used to determine the threshold for identifying potential outliers in a data set.
According to the IQR method:
- Any data point below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is considered a suspected outlier.
This criterion helps in identifying values that are significantly far from the central tendency of the data set. However, the choice of the multiplier (e.g., 1.5, 2, 2.5) can vary depending on the specific requirements of the analysis or the nature of the data being studied.
That's hard for me to understand
I apologize for the confusion. Let me explain it in simpler terms:
When we calculate the interquartile range (IQR), we are looking at the middle 50% of the data. To determine outliers using the IQR method, we use a rule that considers data points that are significantly further away from the central part of the data set.
The multiplier of 1.5 is a commonly used value in statistics to identify potential outliers. When we multiply 1.5 by the IQR, we are setting a threshold for how far a data point can be from the median before it is considered an outlier.
In simpler terms, if a data point is below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR, it is flagged as a potential outlier. This helps us recognize values that are unusually high or low compared to the majority of the data.
I hope this clarifies things for you. Let me know if you have any more questions.