Exercises - Measures of Center and Spread

  1. Given the data set $1, 1, 2, 3, 5, 8$, find the mean, median, mode, and midrange.

  2. For the data set $1, 1, 2, 3, 5, 8$, what is the range, variance, and IQR?

  3. For the following data set: $$\begin{array}{ccccc} 171 & 186 & 191 & 204 & 235\\ 173 & 186 & 193 & 204 & 239\\ 174 & 186 & 197 & 209 & 240\\ 181 & 187 & 199 & 210 & 242\\ 182 & 188 & 200 & 211 & 243\\ 184 & 191 & 200 & 218 & 320\\ \end{array}$$

    1. What is the standard deviation?
    2. What percentage of the data lies within 1 standard deviation of the mean?
    3. What percentage of the data lies within 2 standard deviations of the mean?
    4. Is your answer to part (c) consistent with Chebyshev's Theorem?
    5. What percentage of the data lies within 3 standard deviations of the mean?
    6. Is your answer to part (e) consistent with Chebyshev's Theorem?
    7. Are there any outliers? (use both rules for determining outliers)

  4. For a distribution with a mean of 80 and a standard deviation of 10, at least what percentage of values will fall

    1. between 60 and 100?
    2. between 65 and 95?

  5. Find the smallest integer $x$, such that $x$ is an outlier of the data set $1,2,3,4,5,6,7,8,10,11,x$. Use both rules for determining outliers and compare the results (they will give different answers).