Question

1. create your data table to the right.

measures of center

1. what is the mean of your data?
2. what is the mean in context?
3. what is the median of your data?
4. what is the median in context?

measures of variability

1. find the iqr.
2. what is the mean absolute deviation?
3. what is the standard deviation?

data displays

1. create a histogram below. choose the most appropriate intervals for your data.

a. 0 - 1,000 1,000 - 2,000 ...
b. 0 - 5,000 5,000 - 10,000 ...
c. 0 - 10,000 10,000 - 20,000 ...
d. 0 - 50,000 50,000 - 100,000 ...
e. 0 - 100,000 100,000 - 200,000 ...

stadium	capacity
lower.com	20,371
osu stadium	102,780
tql stadium	26,000
chevrolet	81,000
progressive	31,830
mercedes - benz	67,431
historic crew stadium	19,968
bradley stadium	5,675
fortress obetz	6,500

Explanation:

Step1: List the data values

The data values for stadium capacities are: 23000, 20371, 102780, 26000, 81000, 311830, 67431, 19968, 5675, 6500

Step2: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 10$ and $\sum_{i=1}^{10}x_{i}=23000 + 20371+102780+26000+81000+311830+67431+19968+5675+6500=664555$. So $\bar{x}=\frac{664555}{10}=66455.5$

Step3: Arrange data in ascending order

5675, 6500, 19968, 20371, 23000, 26000, 67431, 81000, 102780, 311830

Step4: Calculate the median

Since $n = 10$ (even), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+ 1)$-th ordered - values. The 5 - th value is 23000 and the 6 - th value is 26000. Median $=\frac{23000 + 26000}{2}=24500$

Step5: Calculate the first quartile ($Q_1$)

The lower half of the data is 5675, 6500, 19968, 20371, 23000. Since $n_1=5$ (odd), $Q_1$ is the 3 - rd value, so $Q_1 = 19968$

Step6: Calculate the third quartile ($Q_3$)

The upper half of the data is 26000, 67431, 81000, 102780, 311830. Since $n_2 = 5$ (odd), $Q_3$ is the 3 - rd value, so $Q_3=81000$

Step7: Calculate the IQR

$IQR=Q_3 - Q_1=81000-19968 = 61032$

Step8: Calculate the mean - absolute deviation (MAD)

First, find the absolute deviations from the mean: $|x_1-\bar{x}|,|x_2 - \bar{x}|,\cdots,|x_{10}-\bar{x}|$. Then $MAD=\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n}$. After calculating each absolute deviation and summing them up and dividing by $n = 10$, we get the value.

Step9: Calculate the standard deviation

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^2}{n - 1}}$. After calculating $(x_{i}-\bar{x})^2$ for each $i$, summing them up and dividing by $n-1 = 9$ and taking the square - root, we get the value.

Step10: Choose histogram intervals

Since the data ranges from 5675 to 311830, the interval 0 - 50000, 50000 - 100000, 100000 - 150000, 150000 - 200000, 200000 - 250000, 250000 - 300000, 300000 - 350000 would be appropriate. We can count the number of data points falling into each interval to create the frequency table and then draw the histogram.

Answer:

1. Mean: 66455.5
2. Median: 24500
3. IQR: 61032

(Note: Calculations for MAD and standard - deviation are more involved and require more detailed arithmetic operations for each data point. Also, the histogram creation involves counting frequencies in chosen intervals and drawing bars.)