Question

Use the distribution in the form of the stem-leaf plot.

Stem      Leaves

1                 1478

2              01237888

3                  189          

16/ The mid-point of the third class is

A./   32   B/   36 C/    34.5 D/   35

17/ The median is

A./   24 B/  23 C/ 25   D/ 5

18/ The relative frequency for the third class is:

A./   20%   B/  50% C/    66% D/   40%

19/ The heights of a group of professional basketball players are summarized in the frequency distribution below. Find the mean height from this frequency table.

Height s (in)           Frequency

70-72                            4

73-75                            6

76-78                            8

79-81                            2

A./   75.2 in   B/  76.8 in C/    74.0 in D/   77.5 in

20/ The temperatures ( in ºF ) in a room is recorded at the top of hours are

67, 68, 70 , 5, 77, 77, 78, 80, 78, 79, 74, 74. Choose best answer:

a/  It is a typo

b/  highest temperature is probably 95

c/  5 is not an outlier

d/  5 is an outlier

21/ The variance of 6 washing machines with prices:  $ 800, $784, $ 1,235, $860, $1,036 and $770 is

A/ 196.4 B/   34,295.3 C/ 26,002.7 D/ 185.2

22/ The coefficient of variation ( round to closest %) for the set of data  :

1, 3, 3, 5, 5, 6, 7, 8, 9 ,12, 15, 24  is

A   74% B/ 67% C/ 24% D/ 78 %

23/ Human body temperatures have the mean of 98.2º  and a standard deviation of 0.6º.

Amy’s temperature can be described by z = 0.9. What is her temperature?

A/ 98.2º B/ 97.8º C/   98.7º D/ 99.3º

24/ The upper bound for the outlier for the data set

-11, 14, 22, 22, 22, 23, 31, 31, 42, 44, 44, 75    is

A/  74.5 B/  75 C/ 84 D/   68

  

25/ The box-plot of a data with 5- point summary   2, 6, 8, 11, 18

A/is positive skewed. B/ is negative skewed.

C/ is symmetric D/ perfect skewed

Answer 1

19)

mid point,x	f	Xf
71	4	284
74	6	444
77	8	616
80	2	160
total	20	1504

mean = ΣXf/Σf = 1504/20=   75.2(answer)

20)

quartile , Q1 = 0.25(n+1)th value=   3.25th   value of sorted data
=   68.5  
      
Quartile , Q3 = 0.75(n+1)th value=   9.75th   value of sorted data
=   78  
      
IQR = Q3-Q1 =    9.5  
      
1.5IQR =    14.25  
      
lower bound=Q1-1.5IQR=   54.25  
      
upper bound=Q3+1.5IQR=   92.25  
      
outlier =values outside lower bound and upper bound      
total outlier below lower bound=   1  
total outlier above upper bound=   0  
total outlier =    1  
so, 5 is an outlier.

21)

X	(X - X̄)²
800	13034.03
784	16943.36
1235	102934.03
860	2934.03
1036	14843.36
770	20784.03

	X	(X - X̄)²
total sum	5485	171472.83
n	6	6

mean =    ΣX/n =    5485.000   /   6   =   914.1667
                      
sample variance =    Σ(X - X̄)²/(n-1)=   171472.8333   /   5   =   34,295.3 (answer)

22)

mean =    ΣX/n =    98.000   /   12   =   8.1667
                      
  
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (443.6667/11)   =       6.3509
coefficient of variation,CV=σ/µ=   0.777655 or 78% (answer)

23)

so, X=zσ+µ=   0.900   *   0.6   +   98.2
X   = 98.7   (answer)      

24)

quartile , Q1 = 0.25(n+1)th value=   3.25th   value of sorted data
=   22  
      
Quartile , Q3 = 0.75(n+1)th value=   9.75th   value of sorted data
=   43.5  
      
IQR = Q3-Q1 =    21.5  
      
1.5IQR =    32.25  
      
  
upper bound=Q3+1.5IQR=   75.75 ≈ 75 (answer)