I'm really stuck on this question.
Employee Earnings per
month($)
1 1,200
2 2,600
3 1,800
4 1,450
5 3,500
6 2,800
7 12,500
8 3,200
Which measure of spread is best for the data in the table?
A. range
B. quartiles
C. interquartile range
D. mean absolute deviation
To determine the measure of spread that is most appropriate for the given data, we need to consider the distribution of the data and the presence of outliers.
The range is the simplest measure of spread and represents the difference between the maximum and minimum values in the data set. However, it is highly influenced by outliers and does not provide information about the middle 50% of the data.
Quartiles divide the data into four equal parts, with the first quartile (Q1) representing the lower 25% of the data, the second quartile (Q2) representing the median or middle value, and the third quartile (Q3) representing the upper 25% of the data. This measure provides insights into the spread of the data and is less sensitive to outliers compared to the range.
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). It focuses on the middle 50% of the data, which provides a more robust measure of spread that is less affected by outliers.
Mean absolute deviation (MAD) calculates the average distance between each data point and the mean. It provides a measure of the average dispersion around the mean, but does not take into account the distribution of the data.
Given the options, the best measure of spread for the provided data would be the interquartile range (C). It allows us to analyze the spread within the middle 50% of the data while being less sensitive to outliers.
To determine the best measure of spread for the data in the table, we need to consider the characteristics of each measure.
1. Range: The range is calculated as the difference between the maximum and minimum values in a dataset. In this case, the range would be the difference between the highest earnings (12,500$) and the lowest earnings (1,200$).
2. Quartiles: Quartiles divide a dataset into four equal parts, each containing 25% of the data. The quartiles help identify the spread of the data by examining the values that divide the data set into four parts. The three quartiles are Q1, Q2 (median), and Q3.
3. Interquartile Range (IQR): The interquartile range is the range of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). The IQR is less affected by outliers since it focuses on the middle portion of the data.
4. Mean absolute deviation (MAD): MAD measures the average distance between each data point and the mean of the dataset. It helps in understanding the average dispersion of data from the mean.
Considering the given dataset, the best measure of spread would be the C. interquartile range (IQR). This is because the IQR considers the middle 50% of the data, providing a more robust measure of spread compared to the range, quartiles, and mean absolute deviation. Additionally, the IQR is less sensitive to outliers, which is important for this dataset to avoid extreme values from distorting the result.