Explain,by taking a suitable example,how the arithmetic mean alters by (i) adding a constant k to each term,(ii) subtracting a constant k from each them,(iii) multiplying each term by a constant k and (iv) dividing each term by a non-zero constant k.
Explain,by taking a suitable example,how the arithmetic mean alters by (i) adding a constant k to each term,(ii) subtracting a constant k from each them,(iii) multiplying each term by a constant k and (iv) dividing each term by a non-zero constant k.
Let x1,x2,x3,x4,x5 be the five numbers whose mean is ¯x i.e,=x1+x2+x3+x4+x55=¯x(i)By adding a constant k to each term,then mean=(x1+k)+(x2+k)+(x3+k)+(x4+k)+(x5+k)5=x1+x2+x3+x4+x5+5k5=x1+x2+x3+x4+x55+k=¯x+k(ii)By subtracting a constant term k from each term, then mean=(x1−k)+(x2−k)+(x3−k)+(x4−k)+(x5−k)5=x1+x2+x3+x4+x5−5k5=x1+x2+x3+x4+x55−k=¯x−k(iii)By multiplying each term by k,then mean=kx1+kx2+kx3+kx4+kx55=k(x1+x2+x3+x4+x5)5=k(x1+x2+x3+x4+x5)5=k¯x(iv)By dividing each term by k,thenMean=x1k+x2k+x3k+x4k+x5k5=1k(x1+x2+x3+x4+x5)5=1k¯xHence we see that in each case,the mean is changed.
Let x1,x2,x3,x4,x5 be the five numbers whose mean is ¯x i.e,=x1+x2+x3+x4+x55=¯x(i)By adding a constant k to each term,then mean=(x1+k)+(x2+k)+(x3+k)+(x4+k)+(x5+k)5=x1+x2+x3+x4+x5+5k5=x1+x2+x3+x4+x55+k=¯x+k(ii)By subtracting a constant term k from each term, then mean=(x1−k)+(x2−k)+(x3−k)+(x4−k)+(x5−k)5=x1+x2+x3+x4+x5−5k5=x1+x2+x3+x4+x55−k=¯x−k(iii)By multiplying each term by k,then mean=kx1+kx2+kx3+kx4+kx55=k(x1+x2+x3+x4+x5)5=k(x1+x2+x3+x4+x5)5=k¯x(iv)By dividing each term by k,thenMean=x1k+x2k+x3k+x4k+x5k5=1k(x1+x2+x3+x4+x5)5=1k¯xHence we see that in each case,the mean is changed.
