Question

You Explain it – Percentiles & Quartiles:

The 5^th percentile of the weight of males 36 months of age is 12.0 kg.

The 95^th percentile of the length of newborn females is 53.8 cm.

One variable that is measured by online homework systems is the amount of time a student spends on homework for each section of the text. The following is a summary of the number of minutes a student spends for each section of the text for the fall 2014 semester in a college statistics class at UHWO.

Q1 = 42         Q2 = 51.5         Q3 = 72.5

a)Provide an interpretation of these results.

b)Determine and interpret the interquartile range.

c)Suppose a student spends 2 hours doing homework for a section. Is this an outlier?

d)Do you believe that the distribution of time spend doing homework is skewed or symmetric? Explain your answer.

Answer 1

The 5^th percentile of the weight of males 36 months of age is 12.0 kg

5% of​ 36-month-old males weigh 12.0 kg or​ less, and 95 % of​ 36-month-old males weigh more than 12.0 kg.

The 95^th percentile of the length of newborn females is 53.8 cm.

95​% of newborn females have a length of 53.8 cm or​ less, and 5 % of newborn females have a length that is more than 53.8cm

2)

(a) The middle 50% of students spend between 42 to 72.5
minutes on their homework. 25% of students spend more than 72.5 minutes on their homework where as 25% students spend less than 42 minutes on their homework.
(b) IQR = Q3 - Q1 = 72.5 – 42 = 30.5 minutes
The middle of 50% of all students has a range of 30.5 minutes of time spent on homework.
(c) Observation value lower than Q1-1.5*IQR will be treated as outliers.
Q1=42
Q1-1.5*IQR = 42 - 1.5*30.5 = -3.75
As 2>-3.75, so if a student spent 2 hours doing homework for a section, it will not be treated as an outlier.
(d) Right-skewed because the difference between Q2 and Q1 is less than the difference between Q3 and Q2.

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