Water Consumption. In the report “Water Poverty in Urban India: A Study of Major Cities”, water consumption in domestic households in major cities of India has been explored. Given below is the data collected from a few houses in New Delhi.

Consumption in Liters Frequency (%) Class marks 0–50 10 25 50–100 14 75 100–150 7 125 150–200 5 175 200–250 3 225 250–300 0 275 300–350 1 325

a. Use the grouped-data formulas to estimate the sample mean and sample standard deviation of the days-to-maturity data. Round your final answers to one decimal place.

b. The following table gives water consumed by houses.

333 106 19 74 189 39 46 242 26 85 161 83 224 63 147 55 193 127 207 22 57 94 37 122 37 87 92 172 43 76 92 117 28 44 139 65 75 110 172 98 Using Definitions 3.4 and 3.6 on pages 121 and 130, respectively, gives the true sample mean and sample standard deviation of the water consumed data as 105.0 and 69.8, respectively, rounded to one decimal place. Compare these actual values of x and s to the estimates from part (a). Explain why the grouped-data formulas generally yield only approximations to the sample mean and sample standard deviation for non–single-value grouping.