Answer :
Final answer:
The five-number summary for the provided weight data is determined by ordering the data and identifying key values. The minimum is 114, the first quartile (Q1) is 152.25, the median (Q2) is 152.25, the third quartile (Q3) is 173.75, and the maximum is 202.
Explanation:
The data set provided consists of weights of 18 adults. When asked for a five-number summary, we are essentially finding out five particular values: the minimum, first quartile (Q1), median (Q2), third quartile (Q3) and the maximum.
Firstly, the data needs to be arranged in ascending order: 114, 119, 120, 127, 131, 135, 142, 144, 151, 153.5, 156, 167, 170, 173, 174.5, 179, 182, 202.
Now we can identify the following:
- Minimum – This is the smallest number in the data set, which is 114.
- First Quartile (Q1) – This is the median of the first half of the data, excluding the overall median if the count of data is odd. In this case, the data set has 18 items, making it even. The mid-point occurs between the 9th and 10th value, so the Q1 is the average between 151 and 153.5, which gives 152.25
- Median (Q2) – This is the middle number when the data is listed in order. In this case, the median is between the 9th and 10th value: 151 and 153.5, average to 152.25.
- Third Quartile (Q3) - This is the median of the second half of the data. In this case, it's between the 14th and 15th value, so the third quartile is the average between 173 and 174.5, giving 173.75.
- Maximum – This is the largest number in the data set. Here it is 202.
Learn more about Five-number summary here:
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