Shape and Variability of Data Practice
1. What is the range of this data set?
27, 5, 11, 13, 10, 8, 14, 18, 7
1. 22
2. 7.5
3. 11
4. 16
2. Use the list below to find the lower quartile.
27, 5, 11, 13, 10, 8, 14, 18, 7
1. 7
2. 7.5
3. 8
4. 8.5
3. Use the list below to find the upper quartile.
27, 5, 11, 13, 10, 8, 14, 18, 7
1. 11
2. 13
3. 14
4. 16
4. What is the interquartile range of the data set?
5, 5, 6, 7, 9, 11, 14, 17, 21, 23
1. 7
2. 9
3. 11
4. 13
5. What is the interquartile range of this data set?
4, 5, 7, 9, 10, 14, 16, 24
1. 6
2. 7
3. 8
4. 9
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1. To find the range of a data set, you need to find the difference between the maximum and minimum values. In this case, the maximum value is 27 and the minimum value is 5.
To calculate the range, subtract the minimum value from the maximum value:
Range = Maximum value - Minimum value
Range = 27 - 5
Range = 22
Therefore, the range of this data set is 22.
2. To find the lower quartile, you need to arrange the data set in ascending order.
Arranging the data set in ascending order: 5, 7, 8, 10, 11, 13, 14, 18, 27
Since there are nine data points, the lower quartile is the value at the 25th percentile, which is between the second and third data points.
The lower quartile is 8.
Therefore, the lower quartile of this data set is 8.
3. To find the upper quartile, you also need to arrange the data set in ascending order.
Arranging the data set in ascending order: 5, 7, 8, 10, 11, 13, 14, 18, 27
Since there are nine data points, the upper quartile is the value at the 75th percentile, which is between the seventh and eighth data points.
The upper quartile is 18.
Therefore, the upper quartile of this data set is 18.
4. The interquartile range is the difference between the upper quartile and the lower quartile.
To calculate the interquartile range, subtract the lower quartile from the upper quartile:
Interquartile range = Upper quartile - Lower quartile
Interquartile range = 18 - 8
Interquartile range = 10
Therefore, the interquartile range of this data set is 10.
5. To find the interquartile range, you first need to find the lower quartile and the upper quartile.
Arranging the data set in ascending order: 4, 5, 7, 9, 10, 14, 16, 24
Since there are eight data points, the lower quartile is the value at the 25th percentile, which is between the second and third data points. The lower quartile is 7.
The upper quartile is the value at the 75th percentile, which is between the sixth and seventh data points. The upper quartile is 16.
To calculate the interquartile range, subtract the lower quartile from the upper quartile:
Interquartile range = Upper quartile - Lower quartile
Interquartile range = 16 - 7
Interquartile range = 9
Therefore, the interquartile range of this data set is 9.
The range is the difference between the largest and the smallest values.
The median is the middle value.
The 1st quartile is the median of the lower half of the values
The 3rd quartile is the median of the upper half of the values
the interquartile range is 3rd quartile minus 1st quartile
Post your work if you get stuck.