U2 is an Irish band that has been popular for over three decades. The lengths of 80 of their songs were selected at random and are listed in the table below. Lengths of Randomly Selected U2 Songs. ?

(seconds) 382 222 214 338 310 559 334 225 177 189 278 300 295 254 331 194 225 294 245 292 262 219 384 336 312 281 308 285 227 258 331 418 195 338 255 225 43 331 179 230 215 252 272 228 281 274 229 178 173 319 267 280 66 186 341 204 253 317 303 337 308 240 252 349 347 94 144 187 272 208 279 276 264 270 286 205 350 444 294 260

a. Use 50-second intervals to make a frequency distribution table for the data.

c. Determine the mean, median, mode, range, and standard deviation for the song lengths. mean (s) median (s) mode (s) range (s) standard deviation (s)

d. Describe whether the data appears to be relatively normally distributed.

e. Assume the data is normally distributed and that the band’s entire collection of songs has a mean and standard deviation equal to those calculated above. What percentage of U2 songs are expected to be

i. over 180 seconds

ii. between 210 seconds and 300 seconds

f. Under what length of time are 90% of all U2 songs expected to be?

1 Answer
Jun 25, 2018

Answer:

Starting you off

Explanation:

I cheated a bit and copied the data into a text document which I then imported into Excel. It was in a row. I transposed it into a column and applied a counting function. The result is below:

This counting approach is very powerful and has many applications.

In G5 I wrote: {=SUM(IF(GivenSeconds>=E5,IF(GivenSeconds<F5,1,0),0))}

'GivenSeconds' is a named range (your data)
The braces tell Excel that we are processing an array. You must not type the braces in. What you do is type

=SUM(IF(GivenSeconds>=E5,IF(GivenSeconds<F5,1,0),0))

Hold down 'shift' and 'Ctrl' then press 'Enter'. The braces are then put in place automatically by Excel.

#color(brown)("Updated Image and calculation: Clarified the type of std deviation.")##color(brown)("You should use the sample standard deviation as shown in the")##color(brown)("second image.")#
Tony B

Tony B