Question

1. Listed below are 20 lengths (in minutes) of randomly selected movies.

(a) Construct a relative frequency histogram to represent the data. Use six classes with a class width of 11, and begin with the first interval class [89, 100), and the second interval class [100, 111), and so on.

90,   92,   94,   94,   95,   96,   105,   108,   110,   116,

117, 119, 119, 120, 125, 132, 132,   136,   149,   154

(b) Calculate the sample mean and the sample standard deviation.

(c) Calculate the first, the second, and the third quartiles of the data, and then construct the box plot of the data.

Answer 1

a)

b)

mean =    ΣX/n =    2303.000   /   20   =   115.1500
                      

                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (6828.55/19)   =       18.9578

c)

  
quartile , Q1 = 0.25(n+1)th value=   5.25th
=   95.25

Median=0.5(n+1)th value =    10.5th
=   116.500
  
Quartile , Q3 = 0.75(n+1)th value=   15.75th
=   130.25

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