Respuesta :
Answer:
Option 3 - This data set has no outliers.
Step-by-step explanation:
Given : The data {70, 67, 66, 65, 66, 78, 68, 71, 80, 78, 72}
To find : Which statement is true about this data set?
Solution :
The statements is all about outlier.
So, we find the outlier of the data.
Step 1- Arranging the data from lowest to highest,
{65,66,66,67,68,70,71,72,78,78,80}
Step 2 - Find the median of the data
As the data is odd numbers so the median is [tex]\frac{n+1}{2}[/tex] th term.
[tex]\frac{n+1}{2}=\frac{11+1}{2}=6th[/tex] term.
6th term is 70 ⇒ Median =70
Step 3 - To find Upper quartile and lower quartile
Lower quartile data set is the median of the upper terms from median
{65,66,66,67,68}
Median of the set is 66
∴ [tex]Q_1=66[/tex]
Upper quartile data set is the median of the lower terms from median
{71,72,78,78,80}
Median of the set is 78
∴ [tex]Q_3=78[/tex]
Step 4 - To find the interquartile range.
[tex]IQR=Q_3-Q_1=78-66=12[/tex]
Step 5 - To find the fences for the data set.
The formula to find range is
[tex][Q_1-1.5(\text{IQR}),Q_3+1.5(\text{IQR})][/tex]
Substitute the values, we get
[tex][66-1.5(12),78+1.5(12)][/tex]
[tex][66-18,78+18][/tex]
[tex][48,96][/tex]
The range in which data lies is [48,96]
We have seen that all the data lie inside the range.
Therefore, This data set has no outliers.
Hence, Option 3 is correct.
