Question

24. Find the mean and median of the above sample and describe its shape. 2 5. For continuous data it is best to use a histogram or a dot plot to graphically describe its shape. 26. For problem #12 list the relative and cumulative relative frequency for each interval. 27. Do the same as #26 for problem #20. 28. Find the standard deviation, range and IQR for the following sample. (3,7,9,11,23,23,37,43,46,54) 29. If the distribution is right-skewed, what is the best measure of center, the mean or the median. 30. If the distribution is bell shaped, (normally distributed) what is the best measure of center, the mean or the median.

Answer 1

SINCE,THE DATA FOR Q24 to Q27 is missing, i am solving from 28

28)

X	(X - X̄)²
3	510.760
7	345.960
9	275.560
11	213.160
23	6.760
23	6.760
37	129.960
43	302.760
46	416.160
54	806.560

	X	(X - X̄)²
total sum	256	3014.4
n	10	10

mean =    ΣX/n =    25.6
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   18.3012
maximum =    54
minimum=   3
  
range=max-min =    51

Median=0.5(n+1)th value =    5.5   th value of sorted data
=   23  
      
quartile , Q1 = 0.25(n+1)th value=   2.75   th value of sorted data
=   8.5  
      
Quartile , Q3 = 0.75(n+1)th value=   8.25   th value of sorted data
=   43.75  
      
IQR = Q3-Q1 =    35.25  

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29) when data is right skewed,median is best measure of center,because median do not get affected by outliers n all

30)

mean and median will be same in bell shaped data

mean is best measure of center for bell shaped distribution