Christy is an avid golf player. Each summer she tries to improve her game by cha

Question

Christy is an avid golf player. Each summer she tries to improve her game by changing golf clubs, trying new techniques, and getting tips from local pros. After each round that she plays at her favourite golf course, Christy records the scores into a database so that she can compile her annual statistics. Use the scores recorded in the graph below to help Christy calculate her statistics for this past season.

(Note: A golf score represents the number of times a player needs to hit a ball to successfully complete the course. The lower the score, the better the performance).

Q6-1: Classify the variable being measured as being one of the following: qualitative nominal, qualitative ordinal, quantitative discrete, or quantitative continuous. What scale of measurement is used to measure this variable? Explain your answer. [1 point]

Q6-2: Calculate the measures of central tendency for Christy’s golf scores for this past season (Show your work): (1) Mean, (2) Median, and (3) Mode. [1 point]

Q6-3: Calculate the measures of variability and position for Christy’s golf scores for this past season: (1) s2X (sample variance), (2) sX (sample standard deviation). [1 point]

Christy's Golf Scores 15 14 13 12 10 80 81 82 83 84 85 86 87 88 89 90 91 92 Score

Explanation / Answer

(1) The scale of measurement is quantitative discrete.
Discrete variables have finite values and these values can be counted. These variables have values of only specific points on a scale.

(2) The frequency distribution, derived from the graph, is given below.

Mean = sum(x * f)/sum(f) = 85.893.
Now, n = sum(f) = 75.
Median = ((n + 1)/2)th term = 38th term = 86.
Mode = score with highest frequency = 87.

(3) Sample variance = sum((x - mean)^2 * f)/n - 1 = 5.583.
Sample standard deviation = square root of sample variance = 2.363.

x (Scores) f (frequency) Cumulative frequency x * f (x-mean)^2 * f 80 1 1 80 34.73 81 3 4 243 71.83 82 3 7 246 45.47 83 5 12 415 41.86 84 9 21 756 32.26 85 7 28 595 5.59 86 13 41 1118 0.15 87 15 56 1305 18.37 88 12 68 1056 53.26 89 4 72 356 38.61 90 2 74 180 33.73 91 0 74 0 0.00 92 1 75 92 37.29

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