High School

A surveyor testing the accuracy of a GPS receiver records the following 30 observations of position errors (in cm):

89.9, 104.0, 93.7, 94.4, 86.0, 115.8, 95.3, 90.7, 88.0, 121.8, 97.4, 95.2, 101.4, 98.2, 97.5, 111.4, 101.6, 103.3, 97.1, 78.7, 85.7, 75.0, 107.5, 106.6, 103.0, 111.5, 99.8, 104.4, 97.3, 100.9.

i. Compute the sample mean and median.
[Hint: Use the sort command in MATLAB.]

ii. Compute the sample standard deviation.

iii. Produce a histogram plot of the data with a bin size of 10 (i.e., the first bin is 70 to 80, the second bin is 80 to 90, etc.).
[Note: This can be sketched on paper or plotted using MATLAB. Either way, having the data sorted (see part i) is helpful.]

Answer :

Final answer:

To compute the sample mean and median, sort the data and apply the relevant formulas. To compute the sample standard deviation, calculate the deviations, square them, and average the squared deviations. To produce a histogram plot, divide the data into bins and count the observations in each bin.

Explanation:

The student is requested to compute the sample mean and median of the given data set using MATLAB. First, the data should be sorted in ascending order using the sort command. After sorting, the sample mean can be computed by summing all the values in the data set and dividing by the number of observations. The sample median can be found by taking the middle value if the number of observations is odd, or by averaging the two middle values if the number of observations is even.

To compute the sample standard deviation, firstly the deviation of each observation from the sample mean should be calculated. Then, these deviations should be squared, and the average of the squared deviations should be computed. Finally, the square root of the average squared deviation gives the sample standard deviation.

To produce a histogram plot of the data with a bin size of 10, the sorted data can be divided into bins with widths of 10. The number of observations falling within each bin can be counted and plotted on a histogram.

Learn more about Sample Statistics here:

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