Answers to Practice Test #1
Answers to Practice Test #1
1. (25 points) Use the following 30 personality test scores to create a frequency distribution with an interval size equal to 5 (i = 5). Please also include in your frequency distribution the real limits, the apparent limits, the frequency, the midpoints, and the relative frequency.
241 242 256 275 283 284 285 290 294 299
241 245 261 277 283 284 289 291 298 299
241 252 268 281 283 285 290 293 299 303
| Real Lim | App. Lim | Frequency | Midpoint | Rel. Freq. |
| 299.5-304.5 294.5-299.5 289.5-294.5 284.5-289.5 279.5-284.5 274.5-279.5 269.5-274.5 264.5-269.5 259.5-264.5 254.5-259.4 249.5-254.5 244.5-249.5 239.5-244.5 |
300-304 295-299 290-294 285-289 280-284 275-279 270-274 265-269 260-264 255-259 250-254 245-249 240-244 |
1 4 5 3 6 2 0 1 1 1 1 1 4 |
302 297 292 287 282 277 272 267 262 257 252 247 242 |
.033 .133 .167 .100 .200 .067 .000 .033 .033 .033 .033 .033 .133 |
2. (20 points)Use the following frequency distribution of the scores from 200 students on a language competency exam to plot a frequency polygon and a cumulative percent polygon. (Note: Make sure that you label all axes with both numeric and alphanumeric labels.)
Real Lim App Lim
F C%
Midpoint
____________________________________
724.5-749.5 725-749
15 100
737
699.5-724.5 700-724
15 92.5
712
674.5-699.5 675-699
20 85
687
649.5-674.5 650-674
25 75
662
624.5-649.5 625-649
25 62.5
637
599.5-624.5 600-624
20 50
612
574.5-599.5 575-599
20 40
587
549.5-574.5 550-574
15 30
562
524.5-549.5 525-549
20 22.5
537
499.5-524.5 500-524
25 12.5
512
3. (30 points) Compute the mean, median, mode, variance and standard deviation of the following scores.
36, 87, 23, 65, 45, 89, 36, 23, 52, 23
Median = (45+36)/2 = 40.5 Hint: Rank the scores before finding the 2 middle scores
Mode = 23
Variance = S2
= 5678.9/9 =
630.989 (Deviation Formula)
or
(Computational Formula)
4. (25 points) A psychological test has a mean of 300 and a standard deviation of 25. Please use these values to compute what proportion of the people taking this test:
A. Score above 347
Z = (347-300)/25 = 1.88.....Col 3 value = .0301
B. Score below 279
Z = (279-300)/25 = -.84.....Col 3 value = .2005
C. Score above 290
Z = (290-300)/25 = -.40.....Col 2 value + .5000 = .1554 + .5000 = .6554
D. Score between 310 and 325
Z310 = (310-300)/25 = .40.....Col 2 value = .1554
Z325 = (325-300)/25 = 1.00.....Col 2 value = .3413
Subtract Col 2 values = .3413-.1554 = .1859
In addition please tell what raw score is the:
E. 33rd percentile
Area below = 33/100 = .33
From Table P......Z = -.4399 (Z is negative because area below is < .50)
X = 300+(-.4399 · 25) = 300-10.998 = 289.002
Copyright © 2004 by Mark W. Vernoy