Show that the data (Sales ) collected from the Job Survey among the telephone as
ID: 3046196 • Letter: S
Question
Show that the data (Sales ) collected from the Job Survey among the telephone associates can be approximated by the normal distribution. In doing this, you will need to provide descriptive statistics as well as a chart to show the distribution. Write a summary paragraph based on your findings on the distribution of the sales data.
SALES 42703.84 41672.17 41279.96 43136.41 46200.00 47517.94 46300.00 43693.88 49250.00 41751.39 47326.93 43566.99 45000.00 44841.36 44998.41 42200.00 46843.74 44898.49 50058.05 44058.10 45909.16 44091.24 44290.88 46382.38 46050.00 43750.00 47200.74 48237.94 47500.00 41446.92 43511.13 51091.30 51157.51 46750.00 48400.00 47578.57 44334.76 49242.79 44964.24 44800.00 38243.33 43533.29 45651.02 48600.00 48788.00 44297.10 41739.38 46700.00 49228.83 47813.80 51100.00 45090.34 43937.31 50050.00 40554.70 47190.80 48300.00 41900.00 45832.08 48600.00 48803.64 43514.37 42988.46 43387.13 48313.51 44626.30 38582.53 51200.00 46221.20 47397.79 42594.44 42700.00 41230.71 43950.00 48700.00 46000.00 41632.71 47500.00 46250.00 45997.34 42717.71 44376.68 46075.91 46750.00 46687.76 44331.24 44343.85 51700.00 46341.83 44963.96 48941.81 48150.51 45450.00 41896.52 46578.33 43260.24 52000.00 45330.73 51100.00 42086.74 46541.97 41516.20 45785.66 43319.39 45498.26 42750.00 39000.00 42434.33 42350.00 39337.15 40531.86 43061.89 40422.95 45565.14 43449.64 39862.21 39880.86 44112.11 45957.58 43747.40 50820.34 47750.00 50483.70 46359.96 48500.00 43574.51 42634.40 46397.06 51300.00 48100.00 46718.84 42699.37 42051.00 44073.14 47237.58 44693.65 47848.74 43043.80 43168.67 46781.17 50262.42 50050.00 40078.60 42621.47 42050.10 40262.70 44808.96 44629.71 47603.27 46088.15 44798.24 48700.00 44037.54 42842.68 44850.14 49345.41 46276.35 43332.44 45111.05 44994.89 44800.00 42209.50 45750.00 45000.00 45750.00 45190.25 45844.08 45849.27 47660.00 46034.38 48921.18 42850.00 50500.00 42389.58 49452.20 43600.00 46050.00 46320.51 47182.48 42110.41 45604.50 48492.56 44600.00 45400.00 45130.95 45723.76 41867.65 43675.58 40349.99 44800.90 43750.00 43843.88 45003.44 48337.28 48309.13 40586.52 42645.47 42888.99 48300.00 43285.71 41076.58 45600.00 45800.00 43505.62 51400.00 42371.64 45200.00 41768.41 48550.00 46700.00 46090.91 46700.00 51800.00 46504.37 49292.54 45640.50 51500.00 52000.00 45727.03 40725.39 48700.00 42289.12 43833.77 42087.12 39842.34 46100.00 43545.58 41750.00 48500.00 42411.96 43207.17 48442.54 41131.25 41586.70 45237.13 45688.48 41530.29 44128.07 43950.00 48950.00 39990.11 43480.74 43869.32 46584.88 46250.00 44918.39 44810.10 42200.00 47977.24 43553.19 47450.00 44836.12 51500.00 43537.78 41501.60 49200.00 41752.14 48670.73 40979.50 46566.60 45800.00 48200.00 48763.12 45284.00 39529.96 46343.08 48969.56 45062.66 48300.00 45600.00 46150.00 42778.50 48500.00 43750.00 48290.94 47756.93 45992.24 43023.07 41284.86 51652.51 42296.89 42350.00 40043.61 44600.00 46432.41 45250.86 46350.00 45500.00 43400.60 43800.00 43614.13 41350.00 42310.88 42490.57 46706.55 42350.00 47303.04 45000.00 48396.96 42373.83 36601.33 48800.00 45177.03 45600.00 44963.79 44200.00 46366.76 48862.82 45806.71 46200.00 43789.71 44549.08 43365.79 46931.30 46720.32 44259.22 44044.24 46000.00 49475.35 45706.06 42916.68 50000.00 43849.53 42727.66 47719.26 43269.48 45174.21 45050.00 44290.60 41362.78 43224.97 46250.00 47757.31 42039.13 43124.12 45491.96 40799.67 42473.72 49642.34 50764.92 43258.30 43350.00 49188.00 44207.93 51500.00 44700.00 44089.34 41395.12 41391.93 42050.03 45600.00 46623.90 43600.00 44587.43 39677.52 41854.92 46079.86 41650.51 46750.00 43150.00 46000.00 43205.29 49550.00 44941.51 44177.21 44376.78 42136.34 41088.38 41650.38 43259.26 46458.41 47720.96 39988.26 43047.48 44020.23 41357.26 43291.50 46858.67 44673.62 48896.08 43722.59 43134.18 42500.19 41049.42 51371.24 43127.26 47481.82 40700.00 49221.41 34577.39 44878.37 41182.79 45155.64 41714.73 44191.49 41667.28 42471.80 42068.82 39059.12 42707.07 44751.21 41596.89 42446.11 42256.24 45198.47 47071.26 43073.31 45378.29 45450.00 47352.21Explanation / Answer
The descriptive statistics for the data is as shown below: -
SALES
Here, as we can see that the mean, median and mode of the data are almost equal which is one of the signs of normally distributed data (in real-world, it is difficult to find perfect normally distributed data). Moreover, we can see that considering the standard deviation, we would be able to find about 68% of the observations within one standard deviation of the mean, 95% observations within two standard deviations of the mean, 99.7% observations within 3 standard deviations of the mean (range is from 34577.39 to 52000).
The descriptive statistics for the data is as shown below: -
SALES
Mean 45001.7744 Standard Error 145.395233 Median 44908.44 Mode 45600 Standard Deviation 2944.02908 Sample Variance 8667307.22 Kurtosis -0.0900756 Skewness 0.13394838 Range 17422.61 Minimum 34577.39 Maximum 52000 Sum 18450727.5 Count 410 Confidence Level(95.0%) 285.815196Related Questions
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