Question

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Answer 1

familiar with box and whisker plots right ?

Answer 2

easy - start by sorting the given data in increasing order

Answer 3

Excellent ! below is the format for five number summary :
`minimum -- IQR1 -- median -- IQR3 -- maximum`

Answer 4

finding minimum and maximum is trivial, just take the first value for minimum and the last value for maximum

Answer 5

Right, what about the other three measures ? know how to find them ?

Answer 6

Inter Quartile Range 1

I think its also called as 25th percentile or Q1

Answer 7

Q1, median and Q2 are just numbers

may be watch this short video from khan :
https://www.youtube.com/watch?v=BXq5TFLvsVw

It explains clearly how to calculate the 3 numbers

Answer 8

Okay, I'll try...

lets find the `median` first

Answer 9

median = middle value of the data set

Answer 10

15, 27, `28, 34`, 42, 52

Answer 11

take average of those two middle numbers to get the median

Answer 12

median = \(\large \dfrac{28+34}{2} = ?\)

Answer 13

Yes !

Answer 14

Q1 = middle value of first half

Answer 15

`15, 27, 28`, 34, 42, 52

Answer 16

whats the middle value of first half ?

Answer 17

Yep !!

Q3 = middle value of second half
15, 27, 28, 34, 42, 52
Q3 = ?

Answer 18

Correct ! its called Q3

Answer 19

Looks like we got all the 5 numbers ?

Answer 20

arrange them in below format :

`minimum -- Q1-- median -- Q3-- maximum`

Answer 21

Looks good ^

Answer 22

we're done with part a

Answer 23

mean = (sum of all values)/(number of values)

Answer 24

Add up all the values,
then divide by the number of values

Answer 25

how ?

Answer 26

check ur addition again
28 +34 +27+ 42+ 52+ 15 = 198
NOT 128

Answer 27

Oh I see, I should have told you what to add lol

Answer 28

Exactly !

Answer 29

Yes, mean = 33

Answer 30

right !

Answer 31

yes please

Answer 32

Notice that there are 3 columns in the given table

Answer 33

Fill the first column with the given data values

Answer 34

x
--------------
28
34
27
42
52
15

Answer 35

order doesn't matter... just take the given data set as it is..

Answer 36

yea, lets figure out what to put in second column

Answer 37

\(\overline{X} = \text{mean} = 33\)

Answer 38

yes !

Answer 39

put it in the table next to x column

Answer 40

x x-33
--------------
28 -5
34 1
27 -6
42 9
52 19
15 -18

Answer 41

square each value in second column

Answer 42

right

Answer 43

Looks good

Answer 44

add them and you're done !

Answer 45

25
1
36
81
361
324
-----------

Answer 46

we use the result from part C for calculating standard dviation

Answer 47

standard deviation = \(\large \sqrt{\dfrac{(x-\overline{x})^2}{n}}\)

Answer 48

\(n\) = number of values in the data set

Answer 49

how ?

Answer 50

standard deviation = \(\large \sqrt{\dfrac{(x-\overline{x})^2}{n}} = \sqrt{\dfrac{828}{6}} = \sqrt{138} \approx 11.75\)

Answer 51

standard deviation = \(\large \sqrt{\dfrac{\color{red}{\sum} (x-\overline{x})^2}{n}} = \sqrt{\dfrac{828}{6}} = \sqrt{138} \approx 11.75 \)

Answer 52

np :)

Answer 53

I'll try, ask...