1. (4 marks) To quantify the variability of a measurement, we often use a quantity called the variance. The variance of n numbers in a dataset can be calculated using the following steps: 1) Calculate the average (or mean) of the n values. We can call this value X (pronounced "X bar"). 2) Compute the difference between each observation and X. Square each of these differences. 3) Compute the sum of these squared differences, and then divide it by n - 1. An example calculation is demonstrated in the section called Measurements, Accurate and Inaccurate in Chapter 8 of the textbook. Suppose we weigh an apple using a kitchen scale. We measure the weight 4 times, and we obtain the values: 71.1 grams, 70.7 grams, 68.2 grams, 70.0 grams a. Calculate the variance of these four measurements. Remember to show all your work. b. You then use a different kitchen scale to weigh the same apple 4 more times, and you obtain the following measurements: 69.2 grams, 72.0 grams, 67.6 grams, 71.2 grams Calculate the variance of the four measurements using this new kitchen scale. Which of the two scales is more precise? Explain your answer clearly