Question

7. Use the following collection of 30 test scores: 100, 65, 67, 61, 62, 70, 75, 73, 88, 77, 83, 79, 95, 79, 80, 102, 86, 87, 87, 91, 87, 89, 92, 90, 99, 87, 72, 93, 79,52 a. Construct a frequency distribution table using 6 classes: include classes, frequencies, class marks, class boundaries, relative frequencies and relative percentages. b. Find the mean to the nearest tenth and sample standard deviation to the nearest tenth. c. Use the results from part b to determine the 2-score associated with a data value of 79.

Answer 1

here minimum observation is sz maximum observation is 102 Range = max amin - -- Tso given use classes - 16 classwidth = Range classes - Classes with class width 8 gore 52-60 61-69, 70- 78, 79-87, 88-96, 97-los Class Marks - 52-60 Class marks for class class mark Setro simillarly for all classes, Class boundaries! find ditterence D to find class boundaries.

D = lower limit of next class Upper limit of previous class D substract from lower limit and add to upper limit at each dass Then we get class boundaries are 51.5-60.5 60.5-69.5, 89.5-78.5, 78.5-87.5,87.5-965 96.5-105.5 Relative frequency Relative frequency Class frequency Total frequency Relative percentage Relative Percentage = Relative frequency Xloo

b Mean = {xi 2447 n 30 - 81.566667 81.6 Sample standard deviation (S.D) S.D. Exi2 - 1({x;)2 204023 - (244772 proc 300 30

- 12.358672 2 12.4 > Mean = 81.6 Sample standard deviation = 12.4 c] Lind a score with data value 79 Zscore = x-thean S.D. 19- 81.6 12.4 0.209677 Answer: Z-score associated with a data value of 79 is F0.209677