Short Answer The median annual salary of the 6 vice-presidents of AVCO Inc. is $150 000. What will this median be if only the highest paid vice- president receives a $50 000 raise? A set of 13 different numbers has a median of 44. If the smallest number in this set is 10, how many of the numbers are greater than 10 but smaller than 44? The variance of a set of data is 13.2. Find the standard deviation to one decimal place. The standard deviation of the lifespan of a collection of batteries is 10 h. What would the standard deviation be if each of the batteries had half of its original lifespan? The Smiths are very particular about their choice of pets. They select kittens on the basis of 3 qualities: cuteness, fluffiness, and attitude. The qualities are given weights 5, 3, and x respectively. Mittens received scores of 8, 9, and 4 in that order for the three qualities. If his weighted mean score was 7.5, what is the value of x, the weight for attitude? A set of 8 numbers has a median of 19. If the numbers are arranged from largest to smallest, what is the sum of the fourth and fifth number? Prove that the sum of the deviations from the mean is always equal to ZEro. Prove that if a number, a, is removed from a set of numbers and it does not change the mean, then the mean equals a. 9. Explain why the variance is never negative. 10. The standard deviation for ungrouped data is given by: E(x - 7) Verify that it is also given by: 2 -2 X - Xx by evaluating each for the set of data 0, 2, 4, 6. Show all steps