1. The problem is to understand how to compute variance and standard deviation using Excel for ungrouped data, and also to understand Z tests, variance, standard deviation, and mean absolute deviation. 2. Variance measures the average squared deviation from the mean. The formula for variance $\sigma^2$ for ungrouped data is: $$\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}$$ where $x_i$ are data points, $\bar{x}$ is the mean, and $n$ is the number of data points. 3. Standard deviation $\sigma$ is the square root of variance: $$\sigma = \sqrt{\sigma^2}$$ It shows how spread out the data is. 4. In Excel, for ungrouped data, variance can be computed using the function =VAR.P(range) for population variance or =VAR.S(range) for sample variance. Standard deviation can be computed using =STDEV.P(range) or =STDEV.S(range). 5. Z test is used to test hypotheses about population means when the population variance is known. - For one sample mean, the Z statistic is: $$Z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$ where $\bar{x}$ is sample mean, $\mu$ is population mean, $\sigma$ is population standard deviation, and $n$ is sample size. - For two sample means, the Z statistic is: $$Z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$ where $\bar{x}_1, \bar{x}_2$ are sample means, $\mu_1, \mu_2$ are population means, $\sigma_1, \sigma_2$ are population standard deviations, and $n_1, n_2$ are sample sizes. 6. Mean Absolute Deviation (MAD) is the average of absolute deviations from the mean: $$MAD = \frac{\sum |x_i - \bar{x}|}{n}$$ It measures average distance from the mean without squaring. 7. To study prelim and midterm test papers, focus on identification questions which often test understanding of these concepts. This explanation covers the requested topics with formulas and Excel functions for practical computation.