Answer to Question #269740 in Statistics and Probability for Zagar

Question

Consumption of Natural Gas: Following data represents the energy consumption of natural gas (in

billions of Btu) by the 30 states and the District of Columbia.

474 475 205 639 197 344 320 409 247 66

377 87 747 166 223 248 958 406 251 346

2391 514 371 58 224 530 317 267 769 91

Part a

Find Arithmetic Mean, Geometric Mean, Harmonic Mean and Root Mean Square (using discrete data values)

Answer 1

$$474, 475, 205, 639, 197, 344, 320, 409, 247, 66,$$

$$377, 87, 747, 166, 223, 248, 958, 406, 251, 346,$$

$$2391, 514, 371, 58, 224, 530, 317, 267, 769, 91$$

$$n=30$$

$$\sum_ix_i=12717$$

$$AM=\dfrac{\sum_ix_i}{n}=\dfrac{12717}{30}=423.9$$

$$GM=(x_1\cdot x_2\cdot x_3\cdot ...\cdot x_n)^{1/n}$$

$$=310.93192470231$$

$$HM=\dfrac{n}{\sum _i\dfrac{1}{x_i}}$$

$$=227.86076562108$$

$$RMS=\sqrt{\dfrac{\sum_ix_i^2}{n}}=598.03090778543$$