The ages in years of the houses on Kelly's block are: 20,26,11,2,28,18,2,27. Find the mean, median and the mode.
Mean: 16.6
Median: 18.20
Mode: 2
Which measures should I use to represent the ages of the houses? Explain.
I'd use the median because the houses that are only 2 years old are outliers.
To represent the ages of the houses on Kelly's block, you should use the mean, median, and mode.
Mean: The mean, which is calculated by adding up all the ages and dividing by the number of houses (in this case, 8), gives you the average age of the houses. This measure provides a representation of the central tendency of the ages in the dataset.
Median: The median represents the middle value of the ages when they are arranged in ascending order. In this case, the median is 18.20, which means that half of the houses are older than 18.20 years and half are younger. The median is useful because it is not influenced by outliers or extreme values, providing a more robust representation of the typical age.
Mode: The mode represents the value that appears most frequently in the dataset. In this case, the mode is 2, indicating that there are two houses with an age of 2 years, which is the most common age on the block. The mode helps identify any patterns or clustering of ages that may be present in the dataset.
Using all three measures together gives a comprehensive representation of the ages of the houses on Kelly's block, considering both the average age (mean), the middle value (median), and the most common value (mode).
To represent the ages of the houses on Kelly's block, you should use a combination of the mean, median, and mode.
1. Mean: The mean is the average of a set of numbers. It is calculated by adding up all the numbers and then dividing the sum by the total number of values. In this case, the mean of the ages would be calculated as follows:
(20 + 26 + 11 + 2 + 28 + 18 + 2 + 27) / 8 = 132 / 8 = 16.6
The mean is useful because it takes into account every value in the dataset and provides a balanced representation of the data. However, the presence of outliers can greatly affect the mean, potentially skewing the result. For example, in this case, the presence of the larger values (such as 26 and 28) pulls the mean upward.
2. Median: The median is the middle value of a set of numbers when they are arranged in numerical order. If there is an even number of values, the median is the average of the two middle values. To find the median of the ages, we need to arrange them in ascending order first:
2, 2, 11, 18, 20, 26, 27, 28
Since there are eight values, the median is the average of the fourth and fifth values (18 and 20):
(18 + 20) / 2 = 38 / 2 = 19
The median is useful because it is not affected by extreme values (outliers) as much as the mean. It gives a clearer representation of the "typical" value in the dataset. In this case, the median is slightly higher than the mean, indicating that the ages of the houses are generally closer to the higher end of the spectrum.
3. Mode: The mode is the value(s) that occur(s) most frequently in a dataset. If there are multiple values that occur with the highest frequency, the dataset is considered multimodal. In this case, we can see that the number 2 appears twice, which is more often than any other number.
The mode is useful because it identifies the most common value(s) in the dataset. It can help identify any patterns or trends present. In this case, the mode is 2, indicating that there are two houses that are at the same age.
By using a combination of mean, median, and mode, you can gain a comprehensive understanding of the ages of the houses on Kelly's block.