Frequency Distributions and Sampling

Frequency Distributions & Sampling The lifestyle data collected and analyzed in this paper are the counts of e-mail messages received (R) and sent (S) on a per-day basis. This paper is a continuation of the study begun in a prior assignment, with the core changes being the inclusion of sample data collected over a period of an additional five days, and analysis of the standard deviation of the data relative to a normal distribution.

For the purpose of this study, each parameter was measured and recorded daily for fifteen consecutive days. Table 1 displays the data collected in sequential, unsorted form.

E-mails Received (R) E-mails Sent (S) Based on the total data collected over a period of 15 days as depicted in Table 1, the following are the measures of central tendency for the number of emails received each day: R: mean: 88.9 median: 81 mode: none Based on the data collected over 15 days as depicted in Table 1, the following are the measures of central tendency for the number of emails sent each day: S: mean: 69.8 median: 64 mode In this section, we compare and contrast the results of the original study having a sample size of ten (10), versus the present cumulative study with a sample size of fifteen (15).

To assist this analysis, Table 2 shows the central tendency calculation results side-by-side for the two studies: Sample Size (N) Mean (R) Mean (S) Median (R) Median (S) Mode (R) Mode (S) 10 56.6 95 55 none 55 15 88.9 69.8 81 64 none 55 Table 2 Is the larger sample changing anything? We observe from Table 2 that with the larger sample size, both the mean and median for both R. And S. have changed. However, the mode has remained unchanged for both R. And S.

Is your mean increasing or decreasing? We observe that the mean for e-mails received (R) has decreased with the larger sample, whereas the mean for e-mails sent (S) has increased with the larger sample.

Do you think the current sample you have is enough to paint an accurate picture, or do you need a much larger sample? Based upon the analysis which follows outlining the normal distribution characteristics of the sample data in Table 1, it would be appropriate to gather additional data to obtain a larger sample size for both R. And S. parameters. A larger sample size would help to reduce the uncertainty whether the distribution of S. is indeed normal, and confirm that R. is not a normal distribution.

Obtaining a sample size of N=30 or greater is a commonly used convention to help ensure that the sample is representative of the population, and that assessments of normal distribution using standard statistical tools are likely to be valid. Using Excel, we have prepared the following frequency distributions for e-mails received (R) and sent (S), using the data in Table 1. Table 3 shows the numeric frequency distributions, and Figure 1 shows these distributions plotted into histograms for each of R. And S.

Because the sample size of N=15 is relatively small, we have selected the bin size to be 25 emails per bin, such that the sample data values are distributed across five bins. A larger number of bins could optionally be selected with larger sample sizes, to help ensure that the frequency distribution is easy to understand for the situation at hand.

E-mails Per day Frequency (R) Frequency (S) 1-25 0 0 26-50 0 3 51-75 6 7 76-100 5 3 101-125 1 2 126-150 3 0 151-200 0 0 Table 3 Figure 1 The standard deviation is a measure of the spread of the distribution of sample data. The standard deviations of R. And S. computed by Excel for the sample size of N=15 are as follows: R: 27.9 S: 21.3 Is this a normal distribution? Based on the graphical histograms generated by Excel in Figure 1, we observe that.