Question

25 , 26 , 26 , 27 , 28 , 31 ,40 ,41

What is the q1 and q3 of this data set

Answer 1

25 , 26 , 26 , 27 , 28 , 31 ,40 ,41

n = total number of data values = 8 ( 8 is even number )

25 , 26 , 26 , 27 , 28 , 31 ,40 ,41

Q2 = median = average of values 27 and 28

Q2 = Median = ( 27 + 28 ) / 2 =    55 / 2 = 27.5

For Q1 consider first half part of the data

25 , 26 , 26 , 27

we have 4 values in first part and 4 is even number so for Q1 we find the average of middle two observation

Q1 = First quartile = Median of ( 25 , 26 , 26 , 27 )

25 , 26 , 26 , 27

Q1 = Average of 26 and 26 = (26+26 )/2 = 52/2 = 26

Q1   = First quartile = 26

For Q3 consider second half part of the data

28 , 31 ,40 ,41

We have 4 value in last part of the data set and 4 is even number -

Q3 =third quartile = average of middle values = ( 31 + 40 )/ 2 = 71 / 2 = 35.5

Q3 = third quartile = 35.5

You can use Ti - 84 or Ti - 83 calculator

Press " Stat "

Select " EDIT "

Select L1

and type given all data values in L1 one by one

Press " STAT "

Select " CALC "

select " 1 - var Stats "

List : L1   ( To type L1 Press " 2ND " and then press # 1 key )

Freq list : ( keep empty as it is " press enter "

Select " calculate " and pres5.5 s enter

Scroll down in output

Q1 = 26

Q2 = 27.5

Q3 = 35.5

Final answer :-

q1 = 26

q3 = 35.5

I hope this will help you :)