Answer:
The values of the box-plot are: B = {8.2, 8.3, 8.4, 8.5 and 8.9}.
Step-by-step explanation:
The data provided is as follows:
X Frequency
8 0
8.1 0
8.2 2
8.3 2
8.4 2
8.5 3
8.6 0
8.7 1
8.8 0
8.9 1
9 0
So, the actual data is:
S = {8.2
, 8.2
, 8.3
, 8.3
, 8.4
, 8.4
, 8.5
, 8.5
, 8.5
, 8.7
, 8.9
}
A boxplot, also known as a box and whisker plot is a method to demonstrate the distribution of a data-set based on the following 5 number summary,
- Minimum (shown at the bottom of the chart)
- First Quartile (shown by the bottom line of the box)
- Median (or the second quartile) (shown as a line in the center of the box)
- Third Quartile (shown by the top line of the box)
- Maximum (shown at the top of the chart).
The data set is arranged in ascending order.
The minimum value is, Min. = 8.2
The lower quartile is,
![[\frac{n+1}{4}]^{th}\ obs.=[\frac{11+1}{4}]^{th}\ obs.=3^{rd }\ obs. =8.3](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bn%2B1%7D%7B4%7D%5D%5E%7Bth%7D%5C%20obs.%3D%5B%5Cfrac%7B11%2B1%7D%7B4%7D%5D%5E%7Bth%7D%5C%20obs.%3D3%5E%7Brd%20%7D%5C%20obs.%20%3D8.3)
,
Q₁ = 8.3.
The median value is,
![[\frac{n+1}{2}]^{th}\ obs.=[\frac{11+1}{2}]^{th}\ obs.=6^{th}\ obs.=8.4](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bn%2B1%7D%7B2%7D%5D%5E%7Bth%7D%5C%20obs.%3D%5B%5Cfrac%7B11%2B1%7D%7B2%7D%5D%5E%7Bth%7D%5C%20obs.%3D6%5E%7Bth%7D%5C%20obs.%3D8.4)
Median = 8.4
The upper quartile is,
![[\frac{3(n+1)}{4}]^{th}\ obs.=[\frac{3(11+1)}{4}]^{th}\ obs.=9^{th }\ obs. =8.5](https://tex.z-dn.net/?f=%5B%5Cfrac%7B3%28n%2B1%29%7D%7B4%7D%5D%5E%7Bth%7D%5C%20obs.%3D%5B%5Cfrac%7B3%2811%2B1%29%7D%7B4%7D%5D%5E%7Bth%7D%5C%20obs.%3D9%5E%7Bth%20%7D%5C%20obs.%20%3D8.5)
,
Q₃ = 8.5.
The maximum value is, Max. = 8.9.
So, the values of the box-plot are: B = {8.2, 8.3, 8.4, 8.5 and 8.9}.
