Frequency Distributions (mod 3 slp) - Essay Example

From the data collected in Module a frequency distribution can be prepared as shown in Table Table Frequency Distribution Time (in Minutes) Frequency81-1001101-1203121-1400141-1603161-1808181-2003201-2202Figure 1: Graph for Frequency DistributionThe distribution resembles a normal distribution as evidenced by the bar and line graphs depicted in Figure 1.Now, to calculate standard deviation, the upper limit and lower limit of each salary range are listed. After this, the mid-point of each salary range is computed.

The product of midpoint of the salary and the frequency is calculated. The sum of all these products (3230) is divided by the total distribution size (20) to compute the mean.Table 2: Calculating Standard Deviation Upper LimitLower LimitMidpoint of SalaryFrequencySumSum of Squares 8110090.5190.58190.25 101120110.53331.536630.75 121140130.5000 141160150.53451.567950.75 161180170.581364232562 181200190.53571.5108870.75 201220210.5242188620.5Sum   203230542825Mean    161.5 Mean Square     27141.

25Variance     1059Std Dev     32.54228019In the last column, the product of frequency and the square of mid-point of salary is computed for each salary range. The sum of all these products is computed (as 542825) and divided by size of the distribution (20) to calculate Mean Square as 27141.25. Variance is computed by subtracting square of mean from Mean square. Variance comes out as 1059. Standard Deviation is found out by calculating the square root of variance. Standard deviation is obtained as 32.54. The calculations are shown in Table 2.

This implies that the distribution can be defined by the mean and standard deviation as (161.5 +/- 32.54).References:Anderson, David R., Sweeny Dennis J. & Williams, Thomas J. (2013). Statistics for Business & Economics. 12th ed.