A student counts the number of seeds produced by ten different haploid Arabidopsis plants and obtains the following data:
0, 5, 15, 25, 100, 150, 200, 600, 1500, 3000.
Which one of the following is the best measure of central tendency for summarizing the above data?​

Correct option is B

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The best measure of central tendency depends on the distribution of the data. Here's a breakdown of the options:

• Mean: The mean is the sum of all the values divided by the number of values. However, the mean can be highly influenced by outliers or extreme values, which is the case here (e.g., 3000), which makes it an unreliable measure in this case. Let's calculate it:
• $\text{Mean}=\; sum\; of\; all\; values/\; no.\; of\; values\; =\; 5595/10$
•  559.5 ~ 560
• As we can see, the mean is 560, which is quite high and does not represent the central tendency well because of the extreme value of 3000.

• Median: The median is the middle value when the data points are arranged in ascending order. Since the data is already in order, the middle values are the 5th and 6th values, which are 100 and 150. The median is the average of these two values:

  $$\text{Median}=\; 100+150/2$$
• $125$
• The median is 125, which is more representative of the central tendency since it is not affected by the extreme values like the mean.

• Mode: The mode is the value that appears most frequently in the data. In this case, all the values are unique, so there is no mode.

• Standard deviation: The standard deviation measures the spread of the data from the mean, not a measure of central tendency.

Since the median is not influenced by the extreme values and better represents the central value in this data set, the median is the best measure of central tendency.

Information Booster:

• Mean is useful when the data is symmetrically distributed and does not contain extreme values. In the presence of outliers, the mean might give a distorted representation of the central tendency.
• Median is a more robust measure of central tendency, especially when the data is skewed or contains outliers. It gives the middle value of the dataset and is unaffected by extreme values.
• Mode is more appropriate for categorical data where we want to know the most frequent value. In continuous data, like this one, it is less informative unless there are repeated values.
• Standard deviation quantifies the spread of the data but does not provide information about where the "center" of the data lies.