Statistics and Probability Problems with Answers

. 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?    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  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).  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  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   AB , A , O , O , AB , B , O , A , AB , O , B , A a) Construct a frequency distribution for the data.  b) If a person is selected randomly from the group of twenty four people, what is the probability that his/her blood type is not O?  Answers to the Above Problems Answers to the Above Questions The given data set has 2 modes: 7 and 9 order data : 3 , 4 , 6 , 7 , 7 , 8 , 9 , 9 , 10 : median = 7 (mean) : m = (3+4+6+7+7+8+9+9+10) / 9 = 7 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)  The standard deviation will increase since 24 is further from away from the other data values than 6. x = 36 , y = 77  median = 75  first quartile = 69  third quartile = 81  interquartile range = 81 - 69 = 12 mean = 70  sample standard deviation = 18.6 (rounded to 1 decimal place) class frequency A 5 B 6 AB 6 O 7 1 - (7/24) = 17/24 = 0.71 (rounded to 2 decimal places)