Asalesperson makes a five percent commission on every sale she makes. her daily sales in dollars) for the past 16 working days were: 28 49 50 34 33 44 35 25 29 30 35 34 32 40 78 39. a) find the 5 number summary and p30 b) find the values of the standard deviation, range, and interquartile range (iqr). c) are there any outliers? explain! .

Step-by-step explanation:

First we arrange these data into ascending order (least to greatest)

25, 28, 29, 30, 32, 33, 34, 34, 35, 35, 39, 40, 44, 49, 50,78

a) 5 number summary :

   Minimum : 25

    = = 31  [median of first half of the data]

   Median : = 34.5

    = = 42  [median of first half of the data]

    Maximum : 78

For we have to use the formula

    where n =  total number of the data

   = = 4.8 ≈ 5

So = 5th term of the data = 32

Minimum : 25,   : 31 Median : 34.5,   : 42, Maximum : 78

b) Standard deviation :

Mean of the data :   = 38.4

Now we will subtract mean and square the result.

25     =   -13.4  = 179.56

28     =   -10.4  = 108.16

29     =   -9.4    = 88.36

30     =    -8.4    = 70.56

32     =    -6.4   = 40.96

33     =    -5.4   = 29.16

34     =    -4.4    = 19.36

34     =    -4.4    = 19.36

35    =     -3.4    = 11.56

35    =   - 3.4    =  11.56

39    =     0.6    = 0.36

40    =    1.6      =  2.56

44    =    5.6     =   31.36

49    =   10.6    =   112.36

50    =  50.6    =   134.56

78     = 39.6     = 1568.16

Now take out mean of those results and find the square root.

=

= 151.75

Now square the result = 12.3186 ≈ 12.32

Range = Maximum - minimum

           = 78 - 25 = 53

Interquartile Range (IQR) =

                                            = 42 - 31 = 11

c) Outliers : The number of the given data there is a number which is far from the other numbers is called outliers that is 78

Outlier = 78

answer: 0.1,0.85

step-by-step explanation: