QUESTION IMAGE
Question
bellow is a list of calories and cholesterol amounts in 4 randomly selected menu items from 4 different fast food companies.
company menu item calories cholesterol (mg)
mcdonald’s bacon, egg, & cheese biscuit 460 215
mcdonald’s big mac® 590 85
mcdonald’s filet - o - fish® 390 30
mcdonald’s cheeseburger 300 40
burger king whopper® sandwich with cheese 740 115
burger king cheeseburger 280 45
burger king crispy chicken sandwich 670 60
burger king bacon, egg & cheese biscuit 400 170
wendy’s baconator® 960 155
wendy’s bacon double stack® 440 65
wendy’s classic chicken sandwich 490 75
wendy’s sausage, egg, and cheese biscuit 580 285
chick - fil - a chicken biscuit 460 45
chick - fil - a bacon, egg, and cheese biscuit 420 180
chick - fil - a grilled chicken sandwich 390 75
chick - fil - a chicken nuggets (8 count) 250 80
a) using your calculator, find the following summary statistics for calroies for each of the companies.
mean min q1 med q3 max std. dev
mcdonald’s 425 300 358
burger king 695 740
wendy’s 617.5 440 470 535 700 960 236.57
chick - fil - a 380 250 320 390 440 460 95.
Step1: Calculate mean for McDonald's
Sum of calories: $460 + 590+390 + 300=1740$. Mean $=\frac{1740}{4}=435$.
Step2: Calculate Q1 for McDonald's
Arrange calories in ascending - order: $300,390,460,590$. $Q1$ is the median of the lower half. Lower half is $300,390$. Median of lower half $=\frac{300 + 390}{2}=345$.
Step3: Calculate median (Med) for McDonald's
Median of $300,390,460,590$ is $\frac{390 + 460}{2}=425$.
Step4: Calculate Q3 for McDonald's
Upper half is $460,590$. Median of upper half $=\frac{460+590}{2}=525$.
Step5: Calculate mean for Burger King
Sum of calories: $740+280 + 670+400 = 2090$. Mean $=\frac{2090}{4}=522.5$.
Step6: Calculate Q1 for Burger King
Arrange calories in ascending - order: $280,400,670,740$. Lower half is $280,400$. Median of lower half $=\frac{280 + 400}{2}=340$.
Step7: Calculate median (Med) for Burger King
Median of $280,400,670,740$ is $\frac{400 + 670}{2}=535$.
Step8: Calculate Q3 for Burger King
Upper half is $670,740$. Median of upper half $=\frac{670+740}{2}=705$.
Step9: Calculate mean for Wendy's
Sum of calories: $960+440+490+580 = 2470$. Mean $=\frac{2470}{4}=617.5$.
Step10: Calculate Q1 for Wendy's
Arrange calories in ascending - order: $440,490,580,960$. Lower half is $440,490$. Median of lower half $=\frac{440 + 490}{2}=465$.
Step11: Calculate median (Med) for Wendy's
Median of $440,490,580,960$ is $\frac{490 + 580}{2}=535$.
Step12: Calculate Q3 for Wendy's
Upper half is $580,960$. Median of upper half $=\frac{580+960}{2}=770$.
Step13: Calculate mean for Chick - fil - A
Sum of calories: $460+420+390+250 = 1520$. Mean $=\frac{1520}{4}=380$.
Step14: Calculate Q1 for Chick - fil - A
Arrange calories in ascending - order: $250,390,420,460$. Lower half is $250,390$. Median of lower half $=\frac{250 + 390}{2}=320$.
Step15: Calculate median (Med) for Chick - fil - A
Median of $250,390,420,460$ is $\frac{390 + 420}{2}=405$.
Step16: Calculate Q3 for Chick - fil - A
Upper half is $420,460$. Median of upper half $=\frac{420+460}{2}=440$.
Step17: Calculate standard deviation for McDonald's
Let $x_i$ be the calorie values. First, calculate the variance. $\bar{x}=435$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 435)^2}{4 - 1}$. After calculation, variance $s^2\approx10366.67$, and standard deviation $s\approx101.82$.
Step18: Calculate standard deviation for Burger King
$\bar{x}=522.5$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 522.5)^2}{4 - 1}$. After calculation, variance $s^2\approx35391.67$, and standard deviation $s\approx188.13$.
Step19: Calculate standard deviation for Wendy's
$\bar{x}=617.5$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 617.5)^2}{4 - 1}$. After calculation, variance $s^2\approx47491.67$, and standard deviation $s\approx217.93$.
Step20: Calculate standard deviation for Chick - fil - A
$\bar{x}=380$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 380)^2}{4 - 1}$. After calculation, variance $s^2\approx7666.67$, and standard deviation $s\approx87.56$.
| Company | Mean | Min | Q1 | Med | Q3 | Max | Std. Dev |
|---|---|---|---|---|---|---|---|
| Burger King | 522.5 | 280 | 340 | 535 | 705 | 740 | 188.13 |
| Wendy's | 617.5 | 440 | 465 | 535 | 770 | 960 | 217.93 |
| Chick - fil - A | 380 | 250 | 320 | 405 | 440 | 460 | 87.56 |
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Step1: Calculate mean for McDonald's
Sum of calories: $460 + 590+390 + 300=1740$. Mean $=\frac{1740}{4}=435$.
Step2: Calculate Q1 for McDonald's
Arrange calories in ascending - order: $300,390,460,590$. $Q1$ is the median of the lower half. Lower half is $300,390$. Median of lower half $=\frac{300 + 390}{2}=345$.
Step3: Calculate median (Med) for McDonald's
Median of $300,390,460,590$ is $\frac{390 + 460}{2}=425$.
Step4: Calculate Q3 for McDonald's
Upper half is $460,590$. Median of upper half $=\frac{460+590}{2}=525$.
Step5: Calculate mean for Burger King
Sum of calories: $740+280 + 670+400 = 2090$. Mean $=\frac{2090}{4}=522.5$.
Step6: Calculate Q1 for Burger King
Arrange calories in ascending - order: $280,400,670,740$. Lower half is $280,400$. Median of lower half $=\frac{280 + 400}{2}=340$.
Step7: Calculate median (Med) for Burger King
Median of $280,400,670,740$ is $\frac{400 + 670}{2}=535$.
Step8: Calculate Q3 for Burger King
Upper half is $670,740$. Median of upper half $=\frac{670+740}{2}=705$.
Step9: Calculate mean for Wendy's
Sum of calories: $960+440+490+580 = 2470$. Mean $=\frac{2470}{4}=617.5$.
Step10: Calculate Q1 for Wendy's
Arrange calories in ascending - order: $440,490,580,960$. Lower half is $440,490$. Median of lower half $=\frac{440 + 490}{2}=465$.
Step11: Calculate median (Med) for Wendy's
Median of $440,490,580,960$ is $\frac{490 + 580}{2}=535$.
Step12: Calculate Q3 for Wendy's
Upper half is $580,960$. Median of upper half $=\frac{580+960}{2}=770$.
Step13: Calculate mean for Chick - fil - A
Sum of calories: $460+420+390+250 = 1520$. Mean $=\frac{1520}{4}=380$.
Step14: Calculate Q1 for Chick - fil - A
Arrange calories in ascending - order: $250,390,420,460$. Lower half is $250,390$. Median of lower half $=\frac{250 + 390}{2}=320$.
Step15: Calculate median (Med) for Chick - fil - A
Median of $250,390,420,460$ is $\frac{390 + 420}{2}=405$.
Step16: Calculate Q3 for Chick - fil - A
Upper half is $420,460$. Median of upper half $=\frac{420+460}{2}=440$.
Step17: Calculate standard deviation for McDonald's
Let $x_i$ be the calorie values. First, calculate the variance. $\bar{x}=435$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 435)^2}{4 - 1}$. After calculation, variance $s^2\approx10366.67$, and standard deviation $s\approx101.82$.
Step18: Calculate standard deviation for Burger King
$\bar{x}=522.5$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 522.5)^2}{4 - 1}$. After calculation, variance $s^2\approx35391.67$, and standard deviation $s\approx188.13$.
Step19: Calculate standard deviation for Wendy's
$\bar{x}=617.5$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 617.5)^2}{4 - 1}$. After calculation, variance $s^2\approx47491.67$, and standard deviation $s\approx217.93$.
Step20: Calculate standard deviation for Chick - fil - A
$\bar{x}=380$. Variance $s^2=\frac{\sum_{i = 1}^{4}(x_i - 380)^2}{4 - 1}$. After calculation, variance $s^2\approx7666.67$, and standard deviation $s\approx87.56$.
| Company | Mean | Min | Q1 | Med | Q3 | Max | Std. Dev |
|---|---|---|---|---|---|---|---|
| Burger King | 522.5 | 280 | 340 | 535 | 705 | 740 | 188.13 |
| Wendy's | 617.5 | 440 | 465 | 535 | 770 | 960 | 217.93 |
| Chick - fil - A | 380 | 250 | 320 | 405 | 440 | 460 | 87.56 |