Observe the following set of data points: [1 2 2 2 3 4 8 9 9 10 10 12]. What is the mean and standard deviation of this data? Are the mean and standard deviation a good summary of the distribution, and why? Calculator allowed.

The mean of the data is calculated simply as the sum of the numbers divided by their count: (1+2+2+2+3+4+8+9+9+10+10+12) / 12 = 6.The standard deviation is the square root of the variance. The variance is the average squared deviation of each datapoint from the mean. To get the deviations, we subtract the mean from each of the data points to get:[-5 -4 -4 -4 -3 -2 2 3 3 4 4 6]Their squares are:[25 16 16 16 9 4 4 9 9 16 16 36]To get the variance we take the mean of these squares, with a calculator I get: 14.6666...Then the standard deviation is the square root of this, which is 3.8297 or therabouts.You could report this mean and standard deviation as a summary statistic of the data, but in this case it is not a good fit, because the mean and standard deviation help to visualise datapoints that are normally distributed, or close to it. The example data given here is bimodal, with two peaks on either side of the mean, but if you report simply the mean and standard deviation then the reader will have no way to know this.