Descriptive Statistics Analysis of Two Data Sets

Nov 18, 2025, 3:16 PM

For each data set below, calculate the following with detailed tables as if made by SPSS: (a) mean

(b) median (c) mode.
– 2, 6, 8, 3, 5, 7, 2, 1, 2
– 85, 12, 23, 23, 45, 54, 65, 45, 1, 34

Descriptive Statistics ("SPSS-style" tables)

Below are the results for each data set. The Case columns represent individual observations, similar to the Data View in SPSS, while the summary table mimics the Descriptives output.
CaseValueCaseValue
12185
26212
38323
43423
55545
67654
72765
81845
9291
1034
StatisticDataset 1Dataset 2
Mean4.038.7
Median3.039.5
Mode223 & 45 (bimodal)

Interpretation

  • Dataset 1 (n = 9) is centered at 4.0. The distribution is slightly right-skewed: the mode is 2, the median 3, and the mean 4.
  • Dataset 2 (n = 10) has a higher center (mean ≈ 38.7). Because two values tie for the highest frequency (23 & 45), the distribution is bimodal. The median (39.5) sits between those two modes.

Visual check

Interactive histograms were displayed above so you can visually inspect the shape and see each case plotted on the x-axis.
Feel free to ask for additional statistics (e.g., variance, standard deviation) or other plots!

task1_40ee0821-a83e-4561-bfd9-ecfa36fe943d.pdf

Missing file

Can you describe the distribution for the dataset 2? Does it resemble bimodal negatively skewed distribution?

Distribution of Dataset 2

StatisticValue
Mean38.7
Median39.5
Modes23 & 45 (two values tie for the highest frequency)
Fisher-Pearson skewness+0.35

Shape inspection

  • Bimodality – yes. Two distinct peaks occur at 23 and 45, giving the distribution a clear bimodal character.
  • Skewness sign – the calculated skewness coefficient is positive (+0.35), indicating a slight right (positive) skew, not a negative (left) one. The long tail extends toward the higher value 85.
  • Visual check – the histogram you just saw confirms this: there are two clusters (around 23 and 45), and a few larger values (54, 65, 85) stretching the right tail.

Conclusion

Dataset 2 should be described as bimodal and mildly positively skewed, rather than bimodal negatively skewed.
Anything else you’d like to explore? For example:
  • Compare this distribution to Dataset 1 with a side-by-side plot.
  • Compute additional dispersion measures (variance, standard deviation).
  • Identify any outliers using box-plots or z-scores.

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