a doubt regarding quartiles and median?

[usmiunique]

ASA,
i wanted to know when to take the mean of the data when calculating the quartiles.
for eg. in M/J/2010 paper 61 stats,
in question 2, we get the following steam-and-leaf diagram.
0|2 5 6 8 8 (5)
1|2 4 6 7 7 9 (6)
2|1 2 3 3 3 5 6 7 (8)
3|1 5 (2)
now in calculating the median, we will divide the total number of data by 2 which in this case is
21/2=10.5 so, which value will we take? 10 th value or 11thvalue or the mean of the 10th and 11th value.
also in calculating the lower quartile, we get 21/4=5.25 here also, do we take the 5th value or the 6th value or the mean of the 5t and 6th value?
again in calculating the upper quartile, we get 21*0.75=15.75 here again do we take the 15th value or the 16th value or the mean of the 15th and 16th value?
sometimes in the mark scheme i have seen them taking the mean and sometimes the value immediately next to it.. im confused as to what should i do?
WILL appreciate any help!

 

[lavanyamane]

ASA,
i wanted to know when to take the mean of the data when calculating the quartiles.
for eg. in M/J/2010 paper 61 stats,
in question 2, we get the following steam-and-leaf diagram.
0|2 5 6 8 8 (5)
1|2 4 6 7 7 9 (6)
2|1 2 3 3 3 5 6 7 (8)
3|1 5 (2)
now in calculating the median, we will divide the total number of data by 2 which in this case is
21/2=10.5 so, which value will we take? 10 th value or 11thvalue or the mean of the 10th and 11th value.
also in calculating the lower quartile, we get 21/4=5.25 here also, do we take the 5th value or the 6th value or the mean of the 5t and 6th value?
again in calculating the upper quartile, we get 21*0.75=15.75 here again do we take the 15th value or the 16th value or the mean of the 15th and 16th value?
sometimes in the mark scheme i have seen them taking the mean and sometimes the value immediately next to it.. im confused as to what should i do?
WILL appreciate any help!

Wait you've got it wrong. The total number is 21, which is an odd number. To find the median for an odd set of values, you do (n+1)/2 th value. So that is 22/2 = 11th value, which is 19. Now for the quartiles: because it is an odd set of values, you find the median and delete it. So, delete 19 in your head. Dvide the res tof the data into 2 equal parts, and the LQ will be the median of the top half and UQ will be the median of the bottom half. Therefore, LQ = 8+12 / 2 = 10 and UQ = 23+25 / 2 = 24. Hope I helped.

 

[solidboy123]

ASA,
i wanted to know when to take the mean of the data when calculating the quartiles.
for eg. in M/J/2010 paper 61 stats,
in question 2, we get the following steam-and-leaf diagram.
0|2 5 6 8 8 (5)
1|2 4 6 7 7 9 (6)
2|1 2 3 3 3 5 6 7 (8)
3|1 5 (2)
now in calculating the median, we will divide the total number of data by 2 which in this case is
21/2=10.5 so, which value will we take? 10 th value or 11thvalue or the mean of the 10th and 11th value.
also in calculating the lower quartile, we get 21/4=5.25 here also, do we take the 5th value or the 6th value or the mean of the 5t and 6th value?
again in calculating the upper quartile, we get 21*0.75=15.75 here again do we take the 15th value or the 16th value or the mean of the 15th and 16th value?
sometimes in the mark scheme i have seen them taking the mean and sometimes the value immediately next to it.. im confused as to what should i do?
WILL appreciate any help!

Yaar suppose ur LQ value is 5.25 take 6 always

 

[Talha]

for odd set of values:-

median: 1/2(n+1)
LQ: 1/4(n+1)
UQ: 3/4(n+1)