Balancing point is the mean
= 23386/30
= 779.53
Value that occurs more than any other value is the mode
Mode =512
Note : we can see that 512 has occurred twice but other values are not repeated
Middle value is the median
n=30 , median is the mean of 15th and 16th observation after arranging in ascending order
Median =(746+785)/2 = 765.5
345 |
379 |
383 |
389 |
477 |
512 |
512 |
525 |
541 |
642 |
687 |
721 |
722 |
744 |
746 |
785 |
794 |
821 |
824 |
864 |
916 |
924 |
942 |
980 |
993 |
1019 |
1126 |
1171 |
1334 |
1568 |
Standard deviation is given by
Calculation
x | (x-xbar)^2 | |
345 | 188816.3 | |
379 | 160424.3 | |
383 | 157236 | |
389 | 152513.7 | |
477 | 91524.4 | |
512 | 71572.3 | |
512 | 71572.3 | |
525 | 64785.52 | |
541 | 56896.56 | |
642 | 18914.5 | |
687 | 8561.801 | |
721 | 3425.761 | |
722 | 3309.701 | |
744 | 1262.381 | |
746 | 1124.261 | |
785 | 29.9209 | |
794 | 209.3809 | |
821 | 1719.761 | |
824 | 1977.581 | |
864 | 7135.181 | |
916 | 18624.06 | |
924 | 20871.58 | |
942 | 26396.5 | |
980 | 40188.22 | |
993 | 45569.44 | |
1019 | 57345.88 | |
1126 | 120041.5 | |
1171 | 153248.8 | |
1334 | 307437 | |
1568 | 621684.9 | |
total | 2474419 |
= 292.10
Skewness is given by
calculation
x | (x-xbar)^3 | |
345 | -82046355.9 | |
379 | -64254737.2 | |
383 | -62348807.3 | |
389 | -59561167.8 | |
477 | -27688877 | |
512 | -19147737.7 | |
512 | -19147737.7 | |
525 | -16489858.6 | |
541 | -13571536.7 | |
642 | -2601311.31 | |
687 | -792223.437 | |
721 | -200509.785 | |
722 | -190407.093 | |
744 | -44852.3934 | |
746 | -37696.468 | |
785 | 163.667323 | |
794 | 3029.741623 | |
821 | 71318.48452 | |
824 | 87943.02262 | |
864 | 602708.7306 | |
916 | 2541625.591 | |
924 | 3015317.293 | |
942 | 4288639.501 | |
980 | 8056532.644 | |
993 | 9727708.549 | |
1019 | 13732618.1 | |
1126 | 41590764.96 | |
1171 | 59992292.43 | |
1334 | 170464582.8 | |
1568 | 490179925.4 | |
total | 436231354.5 |
= 0.60
Kurtosis is given by
calculation
x | (x-xbar)^4 | |
345 | 35651603038 | |
379 | 25735949902 | |
383 | 24723172558 | |
389 | 23260422862 | |
477 | 8376715960 | |
512 | 5122594256 | |
512 | 5122594256 | |
525 | 4197163718 | |
541 | 3237218642 | |
642 | 357758344.3 | |
687 | 73304434.65 | |
721 | 11735837.74 | |
722 | 10954120.05 | |
744 | 1593605.537 | |
746 | 1263962.571 | |
785 | 895.2602568 | |
794 | 43840.36128 | |
821 | 2957577.553 | |
824 | 3910826.216 | |
864 | 50910806.48 | |
916 | 346855644.4 | |
924 | 435622889.3 | |
942 | 696775259.8 | |
980 | 1615093099 | |
993 | 2076573944 | |
1019 | 3288550056 | |
1126 | 14409952335 | |
1171 | 23485182717 | |
1334 | 94517497225 | |
1568 | 3.86492E+11 | |
total | 6.63306E+11 |
kurtosis = 3.14
Coefficient of variation
= (292.10/779.53)*100%
= 37.47 %
Range = highest observation -lowest observation
= (1568-345)
= 1223
QUESTION 9 How much time do Americans living in or near cities spend waiting in traffic,...