find the IQR of the data points
111,121,126,141,198,223,224,238,263,292,327,330
To find the IQR:
1. Put the data in order from least to greatest:
111, 121, 126, 141, 198, 223, 224, 238, 263, 292, 327, 330
2. Find the median (middle value) of the data. If there are an even number of data points, find the average of the two middle values.
Median = (223 + 224) / 2 = 223.5
3. Find the median of the lower half of the data. This is also known as the first quartile (Q1).
Q1 = 126
4. Find the median of the upper half of the data. This is also known as the third quartile (Q3).
Q3 = 327
5. Subtract Q1 from Q3 to find the interquartile range (IQR).
IQR = Q3 - Q1 = 327 - 126 = 201
Therefore, the IQR of the data points is 201.
i think it is 167
We can find the IQR of the data points by following these steps:
1. Order the data points from least to greatest:
111, 121, 126, 141, 198, 223, 224, 238, 263, 292, 327, 330
2. Find the median of the whole data set. Since there are 12 data points, the median is the middle value, which is:
median = (223 + 224) / 2 = 223.5
3. Divide the data set into two halves: the lower half and the upper half. If the median is included in either half, it is not counted again.
Lower half: 111, 121, 126, 141, 198, 223
Upper half: 238, 263, 292, 327, 330
4. Find the median of the lower half, Q1:
Q1 = (126 + 141) / 2 = 133.5
5. Find the median of the upper half, Q3:
Q3 = (292 + 327) / 2 = 309.5
6. Calculate the IQR as the difference between Q3 and Q1:
IQR = Q3 - Q1 = 309.5 - 133.5 = 176
Therefore, the IQR of the data points is 176, not 167.
To find the interquartile range (IQR) of a set of data points, you need to follow these steps:
1. Arrange the data points in ascending order:
111, 121, 126, 141, 198, 223, 224, 238, 263, 292, 327, 330
2. Determine the median (Q2) of the data. Since the data set has 12 points, the middle two values will give us the median. In this case, the middle two values are 223 and 224. Therefore, the median is (223 + 224) / 2 = 223.5.
3. Divide the data set into two halves - the lower half and the upper half. Find the median of the lower half (Q1) and upper half (Q3) separately.
Lower half: 111, 121, 126, 141, 198, 223
Upper half: 238, 263, 292, 327, 330
For the lower half, there are 6 data points. The middle two values are 121 and 126. Thus, Q1 = (121 + 126) / 2 = 123.5.
For the upper half, there are also 6 data points. The middle two values are 292 and 327. Hence, Q3 = (292 + 327) / 2 = 309.5.
4. Calculate the interquartile range (IQR) by subtracting the lower quartile (Q1) from the upper quartile (Q3):
IQR = Q3 - Q1 = 309.5 - 123.5 = 186.
Therefore, the interquartile range (IQR) for the given data points is 186.