Maths Questions

Question

Dot plot shows the number of vehicles per minute crossing an intersection during a period of 20 minutes.

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2 3 4 5 6 7 8 9 10

A) What is the mode?

B) What is the range?

C) What is the median?

D) Where are the scores clustered?

E) Calculate the mean correct to one decimal place.

F) Which score is an outliner?

Answer 1

a) Mode is 7 and 8. Since these occur the most frequently.

b) Range is 8. Max value - min value = 10 - 2 = 8

c) Median is 7. Median is the middle number. Since there are 20 terms, this is found between the 10th and 11th term, which are both 7.

d) Scores are clustered on the right side, which makes the distribution left-skewed.

e) The mean is 6.8. Add up all of the terms and divide by 20: 2 + 4 + 5(3) + 6(2) + 7(5) + 8(5) + 9(2) + 10 = 136. 136/20 = 6.8

f) Although 2 seems like it would be an outlier, there is actually no outlier. Values less than 1.75 or greater than 11.75 are outliers for this distribution. I will show my work below for how I arrived at those numbers:

In order to calculate outliers, we need to find Q1 (which is 1/4 of the way through the data set) and Q3 (which is 3/4 of the way through the data set. Since there are 20 terms, Q1 will be between the 5th and 6th terms and Q3 will be between the 15th and 16th terms. So Q1 is 5.5 and Q3 is 8.

small outlier < Q1 - 1.5(Q3 - Q1)

small outlier < 5.5 - 1.5(8 - 5.5)

small outlier < 1.75

large outlier > Q3 + 1.5(Q3 - Q1)

large outlier > 8 + 1.5(8 - 5.5)

large outlier > 11.75