Knowee
Questions
Features
Study Tools

A survey of 10 fast-food restaurants noted the number of calories in a mid-sized hamburger. The results are given in the table below.Calories in a mid-sized hamburger513 506 501 499 496 506 459 478 463 514Find the mean and sample standard deviation of these data. Round to the nearest hundredth.mean sample standard deviation

Question

A survey of 10 fast-food restaurants noted the number of calories in a mid-sized hamburger. The results are given in the table below.Calories in a mid-sized hamburger513 506 501 499 496 506 459 478 463 514Find the mean and sample standard deviation of these data. Round to the nearest hundredth.mean sample standard deviation

🧐 Not the exact question you are looking for?Go ask a question

Solution

To find the mean (average), you add up all the numbers and then divide by the number of numbers.

Step 1: Add up all the numbers: 513 + 506 + 501 + 499 + 496 + 506 + 459 + 478 + 463 + 514 = 4935

Step 2: Divide by the number of numbers. There are 10 numbers, so: 4935 ÷ 10 = 493.5

So, the mean (average) is 493.5 calories.

To find the sample standard deviation, you first find the variance, and then take the square root of the variance.

Step 1: Find the difference between each number and the mean, square it, and then find the average of these squared differences.

(513 - 493.5)^2 = 380.25 (506 - 493.5)^2 = 156.25 (501 - 493.5)^2 = 56.25 (499 - 493.5)^2 = 30.25 (496 - 493.5)^2 = 6.25 (506 - 493.5)^2 = 156.25 (459 - 493.5)^2 = 1190.25 (478 - 493.5)^2 = 240.25 (463 - 493.5)^2 = 925.00 (514 - 493.5)^2 = 420.25

Add these up and divide by the number of numbers minus 1 (this is what makes it the sample standard deviation rather than the population standard deviation):

(380.25 + 156.25 + 56.25 + 30.25 + 6.25 + 156.25 + 1190.25 + 240.25 + 925.00 + 420.25) ÷ (10 - 1) = 3561.25 ÷ 9 = 395.69

Step 2: Take the square root of the variance to get the standard deviation: √395.69 = 19.89

So, the sample standard deviation is 19.89 calories.

Therefore, the mean is 493.5 calories and the sample standard deviation is 19.89 calories.

This problem has been solved

Similar Questions

Let's shake on it: A random sample of 12-ounce milkshakes from 11 fast-food restaurants had the following number of calories.375 608 473 476 504 510 472700 642 591 580 Send data to ExcelAssume

A study was conducted in which students were asked to estimate the number of calories in a cheeseburger.One group was asked to do this after thinking about a calorie-laden cheesecake.A second group was asked to do this after thinking about an organic fruit salad.The mean number of calories estimated was 770 for the group that thought about the cheesecake and 1027 for the group that thought about the organic fruit salad.Suppose that the study was based on a sample of 20 students in each group,and the standard deviation of the number of calories estimated was 123 for the people who thought about the cheesecake first and 146 for the people who thought about the organic fruit salad first. At the 0.01 level of significance,is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first? Find the test statistic. tsTAT=(Round to two decimal places as needed.)

(c) If appropriate, construct an 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants. Round the answers to at least two decimal places.An 80% confidence interval for the mean calorie count for all 12-ounce milkshakes sold at fast-food restaurants is <<μ.

Henry is in charge of planning a reception for 2200 people. He is trying to decide which snacks to buy. He has asked a random sample of people who are coming to the reception what their favorite snack is. Here are the results.Favorite Snack Number of PeoplePotato chips 26Pretzels 22Cookies 55Other 64Based on the above sample, predict the number of the people at the reception whose favorite snack will be pretzels. Round your answer to the nearest whole number. Do not round any intermediate calculations.people

Question 4Complete the following table. Round each of your answers to 3 significant digits.food energy content when eatencal kcal kJthree ounces of cooked sirloin steak ×2.40105 600 a cup of chicken noodle soup 75.0 a small apple 523.

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.