Answer :
To find the mode, we look for the value(s) that appear most frequently in the data set. In this case, the mode is the number(s) that occur with the highest frequency.
In the given data set: 20, 69, 80, 82, 82, 83, 85, 89, 90, 91, 98.
The mode of this data set is 82 because it appears twice, which is more than any other value in the set.
To find the median, we arrange the numbers in ascending order and find the middle value. If there is an even number of values, we take the average of the two middle values.
Arranging the data set in ascending order: 20, 69, 80, 82, 82, 83, 85, 89, 90, 91, 98.
The median of this data set is the middle value, which is 85. There are five values before and five values after it.
To find the first quartile, we divide the data set into four equal parts, and the first quartile marks the boundary between the lowest 25% and the highest 75% of the data.
The first quartile is the median of the lower half of the data set. In this case, the lower half is: 20, 69, 80, 82, 82.
Arranging the lower half in ascending order: 20, 69, 80, 82, 82.
The first quartile is the median of this lower half, which is 80.
To find the third quartile, we divide the data set into four equal parts, and the third quartile marks the boundary between the lowest 75% and the highest 25% of the data.
The third quartile is the median of the upper half of the data set. In this case, the upper half is: 83, 85, 89, 90, 91, 98.
Arranging the upper half in ascending order: 83, 85, 89, 90, 91, 98.
The third quartile is the median of this upper half, which is 90.
To determine if any data points are outliers, we need to calculate the interquartile range (IQR). The IQR is the difference between the third quartile and the first quartile. Any data point that falls below the first quartile minus 1.5 times the IQR or above the third quartile plus 1.5 times the IQR can be considered an outlier.
In this case, the IQR is 90 - 80 = 10.
To check for outliers, we calculate the boundaries:
Lower bound: 80 - 1.5 * 10 = 80 - 15 = 65
Upper bound: 90 + 1.5 * 10 = 90 + 15 = 105
None of the data points in the given data set fall below 65 or above 105, so there are no outliers in this data set.
The range of the data is the difference between the highest and lowest values in the set. In this case, the range is 98 - 20 = 78.
So, to summarize the answers:
- The mode is 82.
- The median is 85.
- The first quartile is 80.
- The third quartile is 90.
- There are no outliers in this data set.
- The range of the data is 78.
Learn more about range here:brainly.com/question/30339388
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