Question

Q.3 For the following weekly earning distribution of part-time students in the Phoenix area, draw a histogram in Excel and find the following information: a) The Median b) The two quartiles Q1 and Q3 c) The three deciles D2 , D4 and D8 d) The two percentiles P5 and P95 Weekly Earning dollars) Number Of gophers $70-80 80-90 90-100 100-110 110-120 120-130 130-140 140-150 150-160 $160-170 20 115 180 290 204 160 88 74 44 40

Answer 1

For drawing histogram open excel and put the data. Then select the data and go to insert and then go to column and choose 2d column. Then a graph will appear...click on a column of the graph and right click on your mouse and go to format data series option. Then go to Series option and go to the gap and select no gap.. Your Histogram is ready...

a)For median make a new column named cumulative frequency.. I hope you know how to find cumulative frequency. For first data the cumulative frequency is same as it's frequency (number of gophers) which is 20. For the second cumulative frequency is sum of the second and it's preceding frequency which is 20+115 = 135 and so on.

Now for Median find N/2 where N = 1215

In excel to find it press =(the last cumulative frequency/2) and then press enter.

Then you will find N/2 = 607.5 which is less than the cumulative frequency 605...so class with cumulative frequency 605 is median class...

So here XL= 110(lower limit of the median class)

Cf= 315(cumulative frequency of preceding class of median class)

f=290(frequency of median class)

C= 120-110 = 10( difference between two limits of Median class)

Now we will find median by the formula XL+(N/2-cf)/f*c

b) same as median. Just for Q1 you have to find the value of N/4 instead of N2 and for Q3 you have to find the value of 3*N/4

c) same as median. But you have to find the value of 2*N/10 for D2, 4*N/10 for D4 and 8*N/10 for D8 instead of N/2

d) same as median.but you have to find the value of 5*N/100 for P5 and 95*N/100 for P95 instead of N/2