Answer:
minor outlier- 9
mean = 3.75
range is 8
Step-by-step explanation:
The data set would be:
1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 9 = 20 households
To calculate for the outlier in this data set:
Arrange all data points from lowest to highest
Calculate the median of the data set
Calculate the lower quartile and upper quartile
Find the interquartile range
Find the "inner fences" for the data set
So, our data has been arranged. The median of the data set is
1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 9 = 3+4 / 2 = 7/2 = 3.5
Then we go on to find the lower and upper quartile
1, 2, 2, 2, 2, 3, 3, 3, 3, 3, (median) 4, 4, 4, 4, 5, 5, 5, 5, 6, 9
lower quartile upper quartile
median = 2+3 / 2 = 5/2 = 2.5 median = 5+5 / 2 = 10/2 = 5
Then finding interquartile range: upper quartile - lower quartile= 5 -2.5 = 2.5
To find the inner fences: multiply the interquartile range by 1.5. Then, add the result to upper quartile and subtract it from the lower quartile. Thus we have: 2.5*1.5 = 3.75.
add the result to upper quartile = 3.75 + 5 = 8.75
subtract it from the lower quartile = 3.75 - 2.5 = 1
Thus, the two inner fences are (1 - 8.75).
Thus, we can say that 9 is a minor outlier in this distribution and not a major one.
To find the mean :
lets make a table:
Number(x) Frequency (f) fx
1 1 1
2 4 8
3 5 15
4 4 16
5 4 20
6 1 6
9 1 9
summation of fx = 75 summation of frequency is 20.
Mean is summation of fx / summation of frequency = 75/20 = 3.75
Range of data set is the biggest data point - the smallest data point= 9 -1 = 8
