Practice with Statistical Data

To gain your knowledge, you need to have practice your mind first. So this is the example for you..

Problems on statistics and probability are presented. The answers to these problems are at the bottom of the page.

1. Given the data set 
   
   4 , 10 , 7 , 7 , 6 , 9 , 3 , 8 , 9 
   
   Find:
   
   a) the mode, 
   
   b) the median, 
   
   c) the mean, 
   
   d) the sample standard deviation. 
   
   e) If we replace the data value 6 in the data set above by 24, will the standard deviation increase, decrease or stay the same? 

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2. Find x and y so that the ordered data set has a mean of 42 and a median of 35. 
   
   17 , 22 , 26 , 29 , 34 , x , 42 , 67 , 70 , y 

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3. Given the data set 
   
   62 , 65 , 68 , 70 , 72 , 74 , 76 , 78 , 80 , 82 , 96 , 101, 
   
   Find; 
   
   a) the median, 
   
   b) the first quartile, 
   
   c) the third quartile, 
   
   c) the interquartile range (IQR). 

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4. The exam grades of 7 students are given below. 
   
   70 , 66 , 72 , 96 , 46 , 90 , 50 
   
   Find 
   
   a) the mean 
   
   b) the sample standard deviation 

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5. Twenty four people had a blood test and the results are shown below.  A , B , B , AB , AB , B , O , O , AB , O , B , A

Firstly, you try to answer the questions  above. If you not sure your answers, you may look the correct answer on the bottom..

So Good Luck to you!

Answers to the Above Questions

1. 1. The given data set has 2 modes: 7 and 9
   2. order data : 3 , 4 , 6 , 7 , 7 , 8 , 9 , 9 , 10 : median = 7
   3. (mean) : m = (3+4+6+7+7+8+9+9+10) / 9 = 7
   4. 
      

      x	x - m	(x - m)2
      4	-3	9
      10	3	9
      7	0	0
      7	0	0
      6	-1	1
      9	2	4
      3	-4	16
      8	1	1
      9	2	4
      		sum = 44

      
      
      sample standard deviation = 2.35 (rounded to 2 decimal places) 
   5. The standard deviation will increase since 24 is further from away from the other data values than 6.
   
   
2.   x = 36 , y = 77 
3. 1. median = 75 
   2. first quartile = 69 
   3. third quartile = 81 
   4. interquartile range = 81 - 69 = 12
   
   
4. 1. mean = 70 
   2. sample standard deviation = 18.6 (rounded to 1 decimal place)
   
   

1. class	frequency
   A	5
   B	6
   AB	6
   O	7

   
   
2. 1 - (7/24) = 17/24 = 0.71 (rounded to 2 decimal places)