Question

A family goes fishing at a weekend getaway and has a fish fry with their catch. Several of the family members fall sick, and when they were screened in the emergency room, test results show that benzene was consumed by the family members. The fish that were consumed evidently came from a lake that was contaminated. The following data set represents the level of benzene (in micrograms) that each member consumed. Within your response, please explain how you calculated your answer.Given the data set 215, 501, 305, 298, 345, 305, 465, calculate the results below:

a. mean,b. mode,c. median, andd. standard deviation.

Answer 1

a) Mean = 347.71

b) Mode = 305

c) Median = 305

d) Standard deviation = 100.8245

Explanation:

Data set : 215, 501, 305, 298, 345, 305, 465

a) Mean =
`\frac{\textup{Sum of all values}}{\textup{Total number of values}}`

or

Mean =
`\frac{\textup{215 + 501 + 305 + 298 + 345 + 305 + 465}}{\textup{7}}`

or

Mean = 347.71

b) Mode

The value in the set that occurs most often is mode

Thus,

215 298 305 305 345 465 501

Mode = 305

c) Median = The median is the middle number in a sorted list of numbers

215 298 305 305 345 465 501

Hence,

Median = 305

d) Standard deviation

Data Data - mean (Data - mean)²

215 -132.7143 17613.085

501 153.2857 23496.505

305 -42.7143 1824.511

298 -49.7143 2471.511

345 -2.7143 7.367

305 -42.7143 1824.511

465 117.2857 13755.935

====================================

∑ (Data - mean)² = 60993.428

Standard deviation =
`\sqrt\frac{\sum{(Data - mean)^2}}{(n-1)}`

=
`\sqrt(60993.428 )/((7-1))`

= 100.8245