1. Using the Following Frequency Distribution

CHAPTER 3 – DESCRIBING DISTRIBUTIONS IN-CLASS EXERCISE 1. Using the following frequency distribution, Class Interval Exact Limits f cf c% 69-73 68.5-73.5 1 180 100.00 64-68 63.5-68.5 9 179 99.44 59-63 58.5-63.5 14 170 94.44 54-58 53.5-58.5 41 156 86.67 49-53 48.5-53.5 34 115 63.89 44-48 43.5-48.5 35 81 45.00 39-43 38.5-43.5 21 46 25.56 34-38 33.5-38.5 16 25 13.89 29-33 28.5-33.5 7 9 5.00 24-29 23.5-28.5 2 2 1.11

 np  cf    and the following formula (3.1, pg. 48): PX  ll   (w)  f i 

a. Determine P15  (180)(.15)  25  P15  38.5   (5)  21 

b. Determine P45

c. Determine P80 (= 57.04)

th REMEMBER – PX (X percentile) is given a point or percentage (X) and is looking for a score or range of scores. 2. Using the frequency distribution from question 1,  (X  ll)  cf   f  w i  and the following formula (3.2, pg. 50): PRX   (100)  n   

a. Determine PR34  34  33.5   9  (16)  PR   5 (100) 34  180     

b. Determine PR40

c. Determine PR67 (= 97.94)

REMEMBER – PRX (percentile rank of X) is given a score (X) and is looking for a point or percentage of scores.

CHAPTER 3 IN-CLASS EXERCISE 3. Using the following sample of scores:

12 10 12 11 6 15 14 17 9 12 13 8 7 15 14 15 18 19 14 10 14 14 16 8 9

a. Determine the mean X Use Formula 3.4 (pg. 56): X  i n

b. Determine the median Use the guidelines on page 55

c. Determine the mode Use the guidelines on page 54

d. Determine the range Use – (Highest Score – Lowest Score) + 1

CHAPTER 3 IN-CLASS EXERCISE e. Determine the variance Use the Raw Score (or observed score) Formula (3.12, pg. 67) (X )2 X 2  i SS i s 2   n n 1 n 1

f. Determine the standard deviation Use the Raw Score Formula (3.14, pg. 68)

(X ) 2 X 2  i SS i s  s 2   n (n 1) (n 1)

CHAPTER 3 IN-CLASS EXERCISE 4. Provide graphical illustrations for the frequency distributions from which the following measures of central tendency were derived. Describe the distributions in terms of symmetry, indicating the direction of skewness of asymmetric distributions.

a. Mean = 46 Median = 43 Mode = 40

b. Mean = 43 Median = 43 Mode = 43

c. Mean = 40 Median = 43 Mode = 46

5. John too three standardized tests with the following results: Test Score X s Using Formula 3.15 Chemistry 85 82 10 X  X Mathematics 80 75 8 z  English 80 90 12 s

a. Compute a z score for each of John’s test scores.

b. What appears to be John’s strongest subject area?

CHAPTER 3 IN-CLASS EXERCISE