HELP PLEASEEE !!!!1. What is the range of the data set?

45 93 60 72 15 45 81

2. What is the variance of the data set?

63 54 62 59 52

3 . A data set has a variance of 88.

What is the standard deviation of the data set?

Round to the nearest tenth

4 . What is the standard deviation of the data set? Round your answer to the nearest tenth.

6 4 9 5 5 4 5

5 . Which is the box-and-whisker plot for the data set?

11 6 19 14 21 7 13 15 15

Answer with explanation:

Ques 1)

We know that the range of a data set is the difference between the maximum and the minimum value.

We are given a data set as:

45   93    60     72     15     45     81

on arranging the data in the increasing order we get:

15   45    45    60    72    81     93

Minimum value=15

Maximum value=93

Range=Maximum value-Minimum value

Range=93-15

Range=78

Ques 2)

We are given data point as:

63      54      62      59      52

on arranging the data in the increasing order we have:

52    54     59    62     63    

The mean of data is calculated as:

Now we calculate variance

Let mean be denoted by x'

x-x'                    (x-x')²

52-58= -6           36

54-58= -4            16

59-58=1                1

62-58=4               16

63-58=5               25

∑ (x-x')²=94

Now, variance is:

   Variance=∑ (x-x')²/5

                                   =94/5

                                   = 18.8

Hence, variance is: 18.8

Ques 3)

We are given Variance=88

As standard deviation is the square root of variance.

Hence,

standard deviation=√88

                              =9.38

Ques 4)

We arrange the data in the increasing order as:

4    4    5    5    5    6    9

Now mean of the data is:

(x-x')               (x-x')²

-1.43               2.04

-1.43               2.04

-0.43              0.18

-0.43              0.18

-0.43              0.18

0.57               0.32

3.57               12.74

∑ (x-x')²/7=17.68/7=2.52

Hence Variance=2.52

Now standard deviation is the square root of variance.

Hence standard deviation=√2.52=1.6

Ques 5)

The box and whisker plot is attached to the answer.

Minimum value=6

Maximum value=21

Median=14

First quartile=9

Upper quartile=17