Question

For the problems 1 -6

Consider the data set   

16, 26, 31, 32, 32, 32, 42, 47, 47, 47, 50, 50 (already put in increasing order)

Compute the following:

1/   The mode:

A/ 47       B/ 32           C/ Bimodal       D/ 42  

2/   The median:

A/ 42       B/ 37           C/ 32           D/ 47  

3/   The mean:

       A/ 37.7       B/ 37           C/ 36           D/ 36.2

4/   The standard deviation:

       A/ 10.5       B/ 12          C/ 14           D/ 11  

5/   The mid-range:

A./ 17       B/ 20.5         C/ 33           D/ 34      
6/   If x = 42 , the standard deviation s = 12 and the mean = 67, then the z-score ( the standard score) of x is

A./ 2.28       B/ - 1.00       C/ 3.52       D/ -2.08
  
7/   In the set of data : 2, 3, 35, 5, 8, 9,10, 10,12,14,16, is the value 35 outlier?

A/ No, upper limit for outlier is 27.5       B/ Yes, upper limit for outlier is 27.5
C/ No, upper limit for outlier is 24.5       D/ Yes, upper limit for outlier is 32.1
  

For the problems 8 -13: Consider the set of 15 data ( in increasing order )

   10, 15, 19, 20, 21, 21, 29, 29, 30, 30, 33, 39, 40, 50, 50.

( It is better to enter this data set into a calculator to find the needed values to answering the following questions )

8/   Find ( the value x which separates the bottom 30th percentile )      

A./ 70       B/ 21           C/ 29.5         D/ 53      

9/   Find the percentile ( kth percentile ) of the value x = 30.

A/ 53 percentile   B/ 82 percentile C/ 38 percentile   D/ 60 percentile  

10/   The third quartile () is:

   A./ 39       B/ 17           C/ 40         D/ 18      

11/   The inter-quartile range ( IQR) is:          

A./ 17       B/ 21           C/ 19         D/ 59  

12/   The sample variance is approximate to ( round to whole number )

A./ 11       B/ 148       C/ 12         D/ 142
      

13/   Approximate the value of x if its z-score is 0.83 ( Use the formula )

  
A./ 35       B/ 39           C/ 19         D/ 25      
14/   For the data set 8, 6, 29, 3, 9, 23, 15, 18, 5, 3, 22, 27, 4, 2 and 22 the midrange is

  
A./ 16       B/ 11           C/ 15         D/ 18      

15/   By the Empirical Rule, in a city of 62,000 people, the number of people below the mean by more than 1 standard deviation is:

A./ 41,160      B/ 9, 920       C/ 21,080        D/ 6,200      
Questions 16-18 : Use the distribution in the form of the stem-leaf plot

         
Stem   Leaves   

1478   
01237888  
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
  
4
6
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

1) The mode:

C Bimodal ( 32 , and 47 both have 3 frequency)

2)   The median:

C 37 ( 32 + 42 )/2

6) Z-score = (x - u) /s = (42 - 67 ) /12 = -2.08

D) -2.08

7)

PS: We only need to solve first 4 parts according to the guidelines.