Answer:
![Min =78](https://tex.z-dn.net/?f=%20Min%20%3D78)
The maximum is :
![Max = 95](https://tex.z-dn.net/?f=%20Max%20%3D%2095)
Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:
![Median =84](https://tex.z-dn.net/?f=%20Median%20%3D84)
Now we can find the quartile 1 we analyze the first 4 values 78, 80,80, 84 and the first quartile would be:
![Q_1= \frac{80+80}{2}= 80](https://tex.z-dn.net/?f=%20Q_1%3D%20%5Cfrac%7B80%2B80%7D%7B2%7D%3D%2080)
Now we can find the quartile 3 we analyze the last 4 values 84,87, 91, 95 and the third quartile would be:
![Q_3= \frac{87+91}{2}=89](https://tex.z-dn.net/?f=Q_3%3D%20%5Cfrac%7B87%2B91%7D%7B2%7D%3D89)
And finally the 5 number summary would be:
![Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96](https://tex.z-dn.net/?f=%20Min%20%3D%2078%2C%20Q_1%20%3D%2080%2C%20Median%3D84%2C%20Q_3%20%3D%2089%2C%20Max%3D96)
Step-by-step explanation:
We have the following data given:
78, 84, 87, 80, 91, 95, and 80.
The first step is order the dataset on increasing way and we got:
78, 80,80, 84,87, 91, 95
We can begin finding the minimum value and for this case is:
![Min =78](https://tex.z-dn.net/?f=%20Min%20%3D78)
The maximum is :
![Max = 95](https://tex.z-dn.net/?f=%20Max%20%3D%2095)
Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:
![Median =84](https://tex.z-dn.net/?f=%20Median%20%3D84)
Now we can find the quartile 1 we analyze the first 4 values 78, 80,80, 84 and the first quartile would be:
![Q_1= \frac{80+80}{2}= 80](https://tex.z-dn.net/?f=%20Q_1%3D%20%5Cfrac%7B80%2B80%7D%7B2%7D%3D%2080)
Now we can find the quartile 3 we analyze the last 4 values 84,87, 91, 95 and the third quartile would be:
![Q_3= \frac{87+91}{2}=89](https://tex.z-dn.net/?f=Q_3%3D%20%5Cfrac%7B87%2B91%7D%7B2%7D%3D89)
And finally the 5 number summary would be:
![Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96](https://tex.z-dn.net/?f=%20Min%20%3D%2078%2C%20Q_1%20%3D%2080%2C%20Median%3D84%2C%20Q_3%20%3D%2089%2C%20Max%3D96)