Answer :
Outliers: 143, 146, 193, 197. Identified by calculating quartiles, IQR, and comparing values to lower and upper bounds.
To identify outliers in a dataset, one common method is to use the interquartile range (IQR).
Here's how to do it step by step:
1. **Calculate the Quartiles:**
- First, sort the data:
143, 146, 158, 159, 162, 166, 169, 170, 170, 193, 197
- The median (Q2) is the middle value, which is 166.
- The lower quartile (Q1) is the median of the lower half of the data, which is the average of 146 and 159, i.e., (146 + 159) / 2 = 152.5.
- The upper quartile (Q3) is the median of the upper half of the data, which is the average of 170 and 193, i.e., (170 + 193) / 2 = 181.5.
2. **Calculate the Interquartile Range (IQR):**
- IQR = Q3 - Q1 = 181.5 - 152.5 = 29
3. **Identify Outliers:**
- Values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR are considered outliers.
- Lower Bound = Q1 - 1.5 * IQR = 152.5 - 1.5 * 29 = 152.5 - 43.5 = 109
- Upper Bound = Q3 + 1.5 * IQR = 181.5 + 1.5 * 29 = 181.5 + 43.5 = 225
4. **Check which values fall outside the bounds:**
- Outliers are the values that are less than the Lower Bound or greater than the Upper Bound.
Let's check:
- 143 < 109 (Outlier)
- 146 < 109 (Outlier)
- 193 > 225 (Outlier)
- 197 > 225 (Outlier)
So, the outliers in this dataset are 143, 146, 193, and 197.
Answer:
193, 197 are outliers of data.
Step-by-step explanation:
Given : The data set 143, 146, 158, 159, 162, 166, 169, 170, 170, 193, 197 .
To find : Which data values are outliers?
Solution : We have given that 143, 146, 158, 159, 162, 166, 169, 170, 170, 193, 197 .
We need to find Outliers from given data :
Outliers : "Outliers" are values that "lie outside" the other values.
we can see from the data 193 and 197 are lie outside the others values.
Therefore , 193, 197 are outliers of data.
