Question

A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20%; 750; 50%; 658; 306; 550; 40%; 406; 30%; 55%; $1.50; 406; 65; 40%. Assume the underlying distribution is approximately normal.

x = ____ c.

Answer 1

To find the mean and standard deviation of the given data set, calculate the average and standard deviation. The mean can be found by adding up all the values and dividing by the total number of values. The standard deviation can be found by finding the square root of the variance.

Step-by-step explanation:

In order to find the mean (x) and standard deviation (Sx) of the given data, we need to calculate the average of the data set and the standard deviation. The average, or mean, can be found by adding up all the values and dividing by the total number of values. The standard deviation, Sx, can be found by finding the square root of the variance. The variance is found by subtracting the mean from each value, squaring the result, adding up all the squared differences, and dividing by the total number of values. Once we have the variance, we can find the standard deviation by taking the square root.

i. x = (20 + 75 + 50 + 65 + 30 + 55 + 40 + 40 + 30 + 55 + 1.50 + 40 + 65 + 40) / 14 = 40.54 cents

ii. Subtract the mean from each value, square the result, and add up all the squared differences: (20 - 40.54)^2 + (75 - 40.54)^2 + (50 - 40.54)^2 + (65 - 40.54)^2 + (30 - 40.54)^2 + (55 - 40.54)^2 + (40 - 40.54)^2 + (40 - 40.54)^2 + (30 - 40.54)^2 + (55 - 40.54)^2 + (1.50 - 40.54)^2 + (40 - 40.54)^2 + (65 - 40.54)^2 + (40 - 40.54)^2 = 4288.70. Divide by the total number of values: 4288.70 / 14 = 306.34. Take the square root to find the standard deviation: Sx = √306.34 = 17.5 cents.