Descriptive statistics

The first data set (arranged in order) is

5 5 8 10 [15 15] 15 22 28 32

  • The mode is 15 (commonest number)
  • The median is 15 (the middlemost number. Here, as the size of the data set is even, we take the average of the two middle numbers, so ( 15 + 15 ) ⁄ 2.
  • The mean is 15.5 ( 5 + 5 + 8 + 10 + 15 + 15 + 15 + 22 + 28 + 32 ) ⁄ 2.
  • The standard deviation is found using the second method:

     

    Measurement

    (Measurement)2

     

    5

    25

     

    5

    25

     

    8

    64

     

    10

    100

     

    15

    225

     

    15

    225

     

    15

    225

     

    22

    484

     

    28

    784

     

    32

    1024

    Totals

    ∑x = 155

    ∑x2 = 3181

    (∑x)2 = 24025

    (∑x)2 ⁄ n = 2402.5

    n − 1 = 9

    So, s = √( ( 3181 − 2402.5 ) ⁄ 9 ) = 9.30

Second data set

  • The mode is 2
  • The median is 2
  • The mean is 3.4
  • The standard deviation is 2.71

Since the first data set has a mean., mode and median very close to one another, it is likely to have a normal distribution.