Find the mean, median, and mode of the data. Which measure might be misleading in describing the average annual number of visitors who visit these sights? Explain. 4,600,000 , 4,500,000 , 4,000,000 , 4,600,000 , 10,200,000
Mean:
To find the mean, we add up all the values and divide by the number of values:
4,600,000 + 4,500,000 + 4,000,000 + 4,600,000 + 10,200,000 = 28,900,000
28,900,000 ÷ 5 = 5,780,000
The mean annual number of visitors is 5,780,000.
Median:
To find the median, we need to list the values in order from smallest to largest:
4,000,000, 4,500,000, 4,600,000, 4,600,000, 10,200,000
There are an odd number of values, so the median is the middle value:
Median = 4,600,000
The median annual number of visitors is 4,600,000.
Mode:
The mode is the value that appears most frequently in the data set:
The annual number of visitors 4,600,000 appears twice in the data set. The other values appear only once.
Mode = 4,600,000
The mode annual number of visitors is 4,600,000.
The measure that might be misleading in describing the average annual number of visitors is the mean. This is because the outlier value of 10,200,000 is much larger than the other values, and it can skew the mean. In this case, the mean is higher than the median and the mode, which suggests that the outlier is having an effect on the mean. Therefore, the mean might not be a good representation of the typical annual number of visitors.
To find the mean, median, and mode of the given data set, we arrange the numbers in ascending order:
4,000,000, 4,500,000, 4,600,000, 4,600,000, 10,200,000
Mean:
To find the mean, we add up all the numbers and divide by the total number of values. Summing up the numbers, we get:
4,000,000 + 4,500,000 + 4,600,000 + 4,600,000 + 10,200,000 = 27,900,000
Dividing by the total number of values, which is 5, we get:
27,900,000 / 5 = 5,580,000
Therefore, the mean (average) annual number of visitors who visit these sights is 5,580,000.
Median:
The median is the middle value when the data set is arranged in ascending order. In this case, the middle value is:
4,600,000
So, the median annual number of visitors is 4,600,000.
Mode:
The mode is the value that appears most frequently in the data set. Here, the value 4,600,000 appears twice, which is more than any other value. Therefore, the mode is 4,600,000.
Now, considering which measure might be misleading in describing the average annual number of visitors who visit these sights. In this particular case, the measure that might be misleading is the mean (average). The reason being that the presence of an extremely high value (10,200,000) can skew the mean upward significantly. This single outlier greatly affects the overall average and may not accurately represent the typical number of visitors. In this situation, the median or mode may provide a more accurate description of the central tendency of the data.