Question

A company samples the distribution of conductivity in isolation of receptacles and got the following values:

24.46 25.61 26.25 26.42 26.66 27.15 27.31 27.54 27.74 27.94 27.98 28.04 28.28 28.49 28.50 28.87 29.11 29.13 29.50 30.88

Trimming 10% mean when we discard the smallest and largest 10 % of the sample. Can we use that sample for to calculate the point estimate of population mean? What are the values for estimator of population mean with and without trim? Provide full reasoning.

Answer 1

In this question we need to find the sample statistic before trimming the data and after trimming data. I have also plot the histogram showing the distribution of the data.

Sample statistics before trimming the data

sample statistics after trimming the data

10% trimming would mean ( 20*0.1= 2) removing the smallest 2 observations and the largest 2 observation.

Mean without trimming the data = 27.793
Mean with trimming the data = 27.8381

The mean statistic for both datasets is almost equal.
But if we have look at the histogram, we see that without trimming the data, the data seems to be normally distributed. But in the case of the trimmed data, the data not fully represent a normal distribution.

Additional analysis to check outliers and if trimming the data is needed.

We find if there are any outliers in the data.

We find that there are no outliers in the data and hence there is no need to trim the data.