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Question
What is sampling distribution of a statistic?
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Solution
The sampling distribution of a statistic is the probability distribution of a given random sample-based statistic.
It may be considered as the distribution of the statistic for all possible samples from the same population of a given sample size.
For example, the sampling distribution of the mean for n = 2 is given below:
| Sample No. | Outcomes | Sample mean `bar("X")_"i"` |
| 1 | 1, 3 | 2 |
| 2 | 1, 9 | 5 |
| 3 | 3, 9 | 6 |
| 4 | 6, 7 | 6.5 |
| 5 | 7, 10 | 8.5 |
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Use the data in the Table below that relate to monthly household expenditure (in Rs) on the food of 50 households and
| 1904 | 1559 | 3473 | 1735 | 2760 |
| 2041 | 1612 | 1753 | 1855 | 4439 |
| 5090 | 1085 | 1823 | 2346 | 1523 |
| 1211 | 1360 | 1110 | 2152 | 1183 |
| 1218 | 1315 | 1105 | 2628 | 2712 |
| 4248 | 1812 | 1264 | 1183 | 1171 |
| 1007 | 1180 | 1953 | 1137 | 2048 |
| 2025 | 1583 | 1324 | 2621 | 3676 |
| 1397 | 1832 | 1962 | 2177 | 2575 |
| 1293 | 1365 | 1146 | 3222 | 1396 |
Monthly Household Expenditure (in Rupees) on Food of 50 Households
Find the number of households whose monthly expenditure on food is
(b) more than Rs 3000
(c) between Rs 1500 and Rs 2500
