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  1. What is the range of the data set?

45 93 60 72 15 45 81

  1. 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

Verified Answer :

  1. The largest number subtract the smallest number. So it would be 93-15=78

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:

\(Mean=\dfrac{52+54+59+62+63}{5}\\\\\\Mean=\dfrac{290}{5}\\\\\\Mean=58\)

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:

\(Mean(x')=\dfrac{4+4+5+5+5+6+9}{7}\\\\\\Mean=\dfrac{38}{7}\\\\\\Mean(x')=5.43\)

(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

View image virtuematane

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