Question

Exercise 4. Find the mean.and median of the values of the random variable X, whose relativè frequency distribution is given in the following table Relative Frequency 0.18 0.33 0.10 0.06 0.33 4. Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the following boxplot. Exercise 5. 100 110 120 130 140 150 Data Analysis Figure 20 (a) What are the range, the three quartiles, and the interquartile range of the measurements? (b) If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams?

Answer 1

4)

Mean = ∑Px = 2.03

Median:

There are 18 of 0's, 33of 1's, 10 of 2's, 6 of 3's, and 33 of 4's. the middle value is (50^th+51^st)/2 = (1+1)/2=1.

5)

a)

Range = Maximum – Minimum = 146-105 = 41

Q1 = 114

Q2 = 118

Q3 = 126

IQR = Q3-Q1 = 126-114 = 12

b)

Q3 = 126

80^th percentile = 130

Hence, between Q3 ie 75^th percentile and 80^th Percentile there are 5% of observations ie 0.05*800 = 40 observations