Question

Three friends went to a hotel and had breakfast to their taste, paying 16, 17 and 21 respectively 

(i) Find their mean expenditure. 

(ii) If they have spent 3 times the amount that they have already spent, what would their mean expenditure be? 

(iii) If the hotel manager offers 50% discount, what would their mean expenditure be? 

(iv) Do you notice any relationship between the change in expenditure and the change in mean expenditure.

Answer 1

i) Mean expenditure =  \(\frac {Total\, expenditure}{No. \,of\, persons}\)

= \(\frac {16+17+21}{3} = \frac {54}{3} \) = Rs 18

ii) Amount spent = 3 times 

I.e., 3 × 16; 3 × 17; 3 × 21

= Rs. 48; Rs. 51; Rs. 63

Now the average = \(\frac {48+51+63}{3} = \frac {162}{3} \)

= Rs. 54 = 3 x original average

iii) After 50% discount the amount spent is Half of the actual amount = \(\frac {16}{2},\frac{17}{2},\frac {21}{2}\) 

= Rs.8; Rs. 8.50; Rs. 10.50 

Now the average =  \(\frac {8+8.50+10.50}{3} = \frac {27.00}{3} \) = Rs 9 = \(\frac {Original \,average}{2}\)

iv) The change In the observations is also carried out in the mean.