Can someone solve this 6. Following are the published weights (in pound) of all
ID: 3366513 • Letter: C
Question
Can someone solve this
6. Following are the published weights (in pound) of all team members of the San Francisco 49ers from previous year. 177 205 210 210 232 205 185 185 178 210 206 212 184 174 185 242 188 212 215 247 241 223 220 260 245 259 278 270 280 295 275 285 290 272 273 280 285 286 200 215 185 230 250 241 190 260 250 302 265 290 276 228 265 a. Organize the scores from smallest to largest value b. Find the mediarn c. Find the first quartile d. Find the third quartile e. Find the range of the middle 50% (i.e., interquartile range) of the weights f. Assume this is a sample from the San Francisco 49ers football players. Find: i. The sample mean ii. The sample variance and standard deviation ii. The weight that is two standard deviations below the mean iv. Steve, a quarterback, played football, he weighed 205 pounds. How many standard deviations above or below the mean was he? g. The same year, the mean weight for the Dallas Cowboys was 240.08 pounds with a standard deviation of 44.38 pounds. Emmit weighed in at 209 pounds. With respect to their team, who was lighter, Steve or Emmit? How did you determine your answer?Explanation / Answer
Answer (a)
Ordering the data from least to greatest, we get:
174 177 178 184 185 185 185 185 188 190 200 205 205 206 210 210 210 212 212 215 215 220 223 228 230 232 241 241 242 245 247 250 250 259 260 260 265 265 270 272 273 275 276 278 280 280 285 285 286 290 290 295 302
Answer (b)
There are 53 numbers in the data set.
Position of Media = (N+1)/2 = (53+1)/2 = 27
So median will be number at 27th position when data is organized from least to greatest:
174 177 178 184 185 185 185 185 188 190 200 205 205 206 210 210 210 212 212 215 215 220 223 228 230 232 241 241 242 245 247 250 250 259 260 260 265 265 270 272 273 275 276 278 280 280 285 285 286 290 290 295 302
The number at 27th position is 241. Thus, median for the given data set is 241.
Answer (c)
The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. The first half of data set includes all values coming before median in the data set organized from least to greatest.
First Half of Data Set (Sorted):
174 ; 177 ; 178 ; 184 ; 185 ; 185 ; 185 ; 185 ; 188 ; 190 ; 200 ; 205 ; 205 ; 206 ; 210 ; 210 ; 210 ; 212 ; 212 ; 215 ; 215 ; 220 ; 223 ; 228 ; 230 ; 232
There are 26 numbers in first half of data set (sorted)
So first quartile will be average of number at position 13 and 14 in First Half of Data Set (Sorted)
First Quartile = (205+206)/2 = 205.5
Answer (d)
The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. The second half of data set includes all values coming after the median in the data set organized from least to greatest.
Second Half of Data Set (Sorted):
241 ; 242 ; 245 ; 247 ; 250 ; 250 ; 259 ; 260 ; 260 ; 265 ; 265 ; 270 ; 272 ; 273 ; 275 ; 276 ; 278 ; 280 ; 280 ; 285 ; 285 ; 286 ; 290 ; 290 ; 295 ; 302
There are 26 numbers in first half of data set (sorted)
So first quartile will be average of number at position 13 and 14 in Second Half of Data Set (Sorted)
First Quartile = (272+273)/2 = 272.5
We have solved 4 subparts of the given question.