Statistics and Probability Problems with Answers
sample 1

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?


  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


  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).


  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


  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

    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

    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.

  1. x = 36 , y = 77
    1. median = 75
    2. first quartile = 69
    3. third quartile = 81
    4. interquartile range = 81 - 69 = 12

    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)

More References and links

elementary statistics and probabilities.