Brandon J. answered • 06/28/22
High School Math Teacher
a) This distribution is bimodal: 7 and 8 are the mode, since they occur the most frequently
b) The range is the largest value - the smallest value. 10 - 2 = 8
c) The median occurs at the exact middle after the values are ordered from least to greatest. Since there are 20 terms total, the median will be between the 10th and 11 term. Since the 10th and 11th terms are both 7, the median is 7.
d) The data appears to be left-skewed since the tail of the distribution curve is to the left. I believe this is what the question is asking for, but I'm not certain.
e) To find the mean, we need to add up all of the terms then divide by 20 (since there are 20 terms total). 2 + 4 + 5(3) + 6(2) + 7(5) + 8(5) + 9(2) + 10 = 136 and 136/20 = 6.8
f) 2 appears to be an outlier, but there actually is no outlier. I have shown the work below for checking whether of not a number is an outlier.
There is a way to check this mathematically confirm part (f).
low outlier < Q1 - 1.5(Q3 - Q1)
high outlier > Q3 + 1.5(Q3 - Q1)
Q1 is between the 5th and 6th terms, so 5.5
Q3 is between the 15th and 16th terms, so 8
low outlier < 5.5 - 1.5(8 - 5.5)
low outlier < 1.75
high outlier > 8 + 1.5(8 - 5.5)
high outlier > 11.75
So any number less than 1.75 or greater than 11.75 is an outlier. There is no outlier in this data set.
