Three friends went to a hotel and had breakfast to their taste, payin

1.	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» 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.

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»

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.