1 answer

An education statistics organization reported recent average mathematics achievement scores for eighth graders in 50 regions....

Question:

Region Score Region Score 270 285 277 276 270 286 291 282 281 279 274 285 283 287 284 289 279 26 290 282 272 292 294 270 282 286 293 284 274 285 290 279 278 289 275 289 285 294 285 288 269 286 287 28 29 6 31 32 34 35 10 37 38 39 12 15 16 17 41 42 18 27343 288 289 297 276 294 264 288 19 20 21 45 46 47 23 24 25 49 50

An education statistics organization reported recent average mathematics achievement scores for eighth graders in 50 regions. Complete parts a through c below.

a) Find the median, the IQR, the sample mean, and the sample standard deviation of these regional averages.

Region Score Region Score 270 285 277 276 270 286 291 282 281 279 274 285 283 287 284 289 279 26 290 282 272 292 294 270 282 286 293 284 274 285 290 279 278 289 275 289 285 294 285 288 269 286 287 28 29 6 31 32 34 35 10 37 38 39 12 15 16 17 41 42 18 27343 288 289 297 276 294 264 288 19 20 21 45 46 47 23 24 25 49 50

Answers

a) Total number of observations = 50

To find the median,

median will be the average value of (50/2) = 25 and (50/2) + 1 = 26 th observations.

Here, 25th observation = 285 and 26th observations= 285

median = (285 + 285)/2 = 285

b) Similarly, we can find Q1 = 276.75 and Q3 = 289

IQR = Q3 - Q1 = 289 - 276.75 = 12.25

c) sample mean 50 50 ΣΖϊ-282.90

d) sample variance 50 (zi-i)2-59.72 50 1

sample standard deviation 50 50-1 〉 (zi-2)2 = V59.72 = 7.73 S-

.

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