Question

ANOVA (Analysis of Variances)


The following are data cholesterol levels of 60 employees.
X
205 327 189 205 148 139 178 157 188 301
195 185 164 182 201 248 298 264 177 169
174 169 155 188 194 192 177 189 188 176
158 305 248 189 209 159 202 177 278 268
166 285 249 203 199 170 165 180 201 209
301 188 165 173 183 206 202 283 207 156

a. Find the mean, median, mode, and standard deviation for X from the data given below.
b. In the frequency distribution for the data.

Answer 1

Conditions

ANOVA (Analysis of Variances)

The following are data cholesterol levels of 60 employees.

X

Find the mean, median, mode, and standard deviation for X from the data given below.

Solution

The mean:

$$\bar{x} = \frac{1}{n} \cdot \sum_{i=1}^{n} x_i$$

203.433

The standard deviation:

$$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2}, \quad \text{where} \quad \mu = \frac{1}{N} \sum_{i=1}^{N} x_i.$$

45.5577

The median:

In statistics and probability theory, median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values

189

The mode:

The mode is the value that appears most often in a set of data.

188