To find the variability in the distribution of the means, we need to calculate a measure of spread, such as the standard deviation. We can use the dot plot to estimate the standard deviation of the distribution.
From the dot plot, we see that the range of the means is from 0 to 150 bags of dog food sold per day. The midpoint of this range is 75, which we can use as an estimate of the population median. We can estimate the standard deviation by calculating the distance between the median and the quartiles.
From the dot plot, we can see that the lower quartile (Q1) is around 60, and the upper quartile (Q3) is around 110. Therefore, the interquartile range (IQR) is:
IQR = Q3 - Q1 = 110 - 60 = 50
We can use the IQR to estimate the standard deviation by assuming that the distribution is approximately normal and using the empirical rule, which states that:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the IQR is about half of the range, we can estimate the standard deviation as:
SD ≈ IQR / 1.35 ≈ 50 / 1.35 ≈ 37
Therefore, an appropriate estimate of the standard deviation of the distribution of means is 37, rounded to the nearest whole number.
Interpretation: The variability in the distribution of means is relatively large, with a standard deviation of approximately 37 bags of dog food sold per day. This means that the mean number of bags sold per day can vary by as much as 37 bags from one sample to another.