Question

Need help with section 3.10

Exercises 3.9 At their first inaugurations, the first 10 presidents of the United States were 57 61 57 57 58 57 61 54 68 51 years old. Find the mean, median, and mode of the ages of those presidents at their first inauguration 3.10 As part of a laboratory assignment in nutrition, fifteen students determined the number of calories in a serving of lasagna. They obtained the values 329 335 347 318 322 330 351 362 315 342 346 353 316 327 333 ) Find the mean b) Subtract 300 from each value and then find the mean of the numbers thus obtained. Add 300 to the result. Does this suggest a simplification for the calculation of the mean? 3.22 An instructor counts the final examination in a course three times as much as each of the three one-hour examinations. What is the average grade of a student who received grades of 72, 86, and 80 in the three one- hour examinations and 90 in the final examination? 4.10 n five attempts, it took a person 12 18 14 11 15 minutes to change the oil in a particular make of automobile. Calculate the standard deviation of this sample using a) the formula which defines s b) Although the course consists of topics in probability, the initial discussion in the course begins with statistics

Answer 1

(3.9)

The data is 57, 61, 57, 57, 58, 57, 61, 54, 68, 51

The data arranged in the ascending order is 51, 54, 57, 57, 57, 57, 58, 61, 61, 68

Mean = sum of the data/number of data = 581/10 = 58.1 years

Median = middle value = average of 5th and 6th values = (57 + 57)/2 = 57 years

Mode = Most frequent value = 57 years.

(3.10)

The data is 329, 335, 347, 318, 322, 330, 351, 362, 315, 342, 346, 353, 316, 327, 333

Mean = sum of data/number of data = 5026/15 = 335.07

The new data is 29, 35, 47, 18, 22, 30, 51, 62, 15, 42, 46, 53, 16, 27, 33

The new mean = 526/15 = 35.07

Add 300 to this, we get 335.07 which was the original mean.