In: Math
PLEASE SOLVED THIS PROBLEM BY HAND AND IN MINITAB:
The following data are direct solar intensity measurements (watts/m²) on different days at a location in southern Spain: 562, 869, 708, 775, 775, 704, 809, 856, 655, 806, 878, 909, 918, 558, 768, 870, 918, 940, 946, 661, 820, 898, 935, 952, 957, 693, 835, 905, 939, 955, 960, 498, 653, 730, and 753. Calculate the sample mean and sample standard deviation. Prepare a dot diagram of these data. Indicate where the sample mean falls on this diagram. Give a practical interpretation of the sample mean.
The given sample observations are,
562, 869, 708, 775, 775, 704, 809, 856, 655, 806, 878, 909, 918, 558, 768, 870, 918, 940, 946, 661, 820, 898, 935, 952, 957, 693, 835, 905, 939, 955, 960, 498, 653, 730, and 753.
xi | xi-xbar | (xi-xbar)^2 |
562 | -248.514 | 61759.34985 |
869 | 58.48572 | 3420.578859 |
708 | -102.514 | 10509.17863 |
775 | -35.5143 | 1261.264439 |
775 | -35.5143 | 1261.264439 |
704 | -106.514 | 11345.29291 |
809 | -1.51428 | 2.293059061 |
856 | 45.48572 | 2068.950269 |
655 | -155.514 | 24184.69284 |
806 | -4.51428 | 20.37876906 |
878 | 67.48572 | 4554.321729 |
909 | 98.48572 | 9699.436059 |
918 | 107.4857 | 11553.17893 |
558 | -252.514 | 63763.46413 |
768 | -42.5143 | 1807.464429 |
870 | 59.48572 | 3538.550289 |
918 | 107.4857 | 11553.17893 |
940 | 129.4857 | 16766.55039 |
946 | 135.4857 | 18356.37897 |
661 | -149.514 | 22354.52142 |
820 | 9.485715 | 89.97878906 |
898 | 87.48572 | 7653.750329 |
935 | 124.4857 | 15496.69324 |
952 | 141.4857 | 20018.20755 |
957 | 146.4857 | 21458.0647 |
693 | -117.514 | 13809.60718 |
835 | 24.48572 | 599.5502391 |
905 | 94.48572 | 8927.550339 |
939 | 128.4857 | 16508.57896 |
955 | 144.4857 | 20876.12184 |
960 | 149.4857 | 22345.97899 |
498 | -312.514 | 97665.17833 |
653 | -157.514 | 24810.74998 |
730 | -80.5143 | 6482.550089 |
753 | -57.5143 | 3307.892979 |
total | 559830.7429 |
By using minitab,
Dotplot of sample observations