on a rainy day, the kids at camp fox forest built houses out of playing cards. pam recorded the height of…
on a rainy day, the kids at camp fox forest built houses out of playing cards. pam recorded the height of each groups house.\nhouse heights\ncomplete the sentences.\nthe median of the data is _ cards. the range is _ cards. if an outlier were added at 1 card, the ______ would change.\n5 ... 6 ... range\n5 ... 6 ... median\n6 ... 5 ... range\n6 ... 5 ... median
Answer
Explanation:
Step1: Find the number of data - points
There are 7 data - points: 4, 4, 4, 5, 7, 8, 10.
Step2: Calculate the median
Arrange the data in ascending order: 4, 4, 4, 5, 7, 8, 10. Since there are 7 (an odd number) data - points, the median is the $\left(\frac{7 + 1}{2}\right)$-th value. So the median is the 4th value, which is 5.
Step3: Calculate the range
The range is the difference between the maximum and minimum values. The maximum value is 10 and the minimum value is 4. So the range is $10-4=6$.
Step4: Analyze the effect of an outlier
If an outlier is added at 1 card, the minimum value changes from 4 to 1. The median is the middle value of the ordered data - set. Adding 1 will not change the position of the middle value for 8 data - points (the new ordered set is 1, 4, 4, 4, 5, 7, 8, 10 and the median is $\frac{4 + 5}{2}=4.5$ but if we consider the concept for odd - numbered data sets before adding the outlier and the nature of how outliers affect measures, the range will change as the difference between the maximum (10) and minimum (1) is now $10 - 1=9$ instead of 6.
Answer:
5 ... 6 ... range