Question

Consider the data:

40 43 39 35 37 43 46 37

If 1 is added to each data value, which of the following will be unchanged?

(i) median (ii) standard deviation (iii) range

Group of answer choices

Answer 1

(A)

Now , we compute the before adding 1.

(i) First to arrange the given observations in increasing order .

35,37,37,39,40,43,43,46

Since , n=8 and which is even

(ii) The table given below ,

	40	0
	43	9
	39	1
	35	25
	37	9
	43	9
	46	36
	37	9
Total	320	98

The standard deviation is ,

(iii) Range = Largest observation - Smallest observation = 46-35=11

(B)

Now , we again compute after adding 1.

(i) First to arrange the given observations in increasing order .

35+1=36,37+1=38,37+1=38,39+1=40,40+1=41,43+1=44,43+1=44,46+1=47

Since , n=8 and which is even

(ii) The table given below ,

	41	0
	44	9
	40	1
	36	25
	38	9
	44	9
	47	36
	38	9
Total	328	98

The standard deviation is ,

(iii) Range = Largest observation - Smallest observation = 47-36=11

From (A) and (B)

The value of the median will be  changed

The value of the standard deviation and range will be unchanged.