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

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

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.