Answer Key - Activity on Measure of Central tendency, dispersion-converted (pdf)-converted PDF

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Answer Key – Activity on Measures of Central Tendency …

I.

How will you know that a mean is smaller or bigger? Is a mean score 35 smaller than a mean score 60? Answer: If there is only one data set, then mean 60 is bigger.

II.

In an exam of 50 items, the mean of section A is 42 while the mean of section B is 46. How will you compare the performance of the two sections? Answer: Section B has better performance than section A since the mean of section B is bigger than the mean of section A.

III.

You have tested 2 types of battery for your wall clock, battery X and battery Y. Battery X has a life span of 5 months while battery Y has a life span of 9 months. In your next purchase of battery, what band will you choose? Answer: battery Y

IV.

If you are a businessman, how will the mode of products help in your decision making? Answer: Example : Among the sizes of t-shirt , the mode is medium size. As a businessman you need to increase the number of stocks for medium since it is the most preferred size.

V.

Give your interpretation of the following: 1. The median height of young adults in Brgy. 6-C is 5.5 ft. Answer: This means that 50% of young adults in Brgy 6-C have heights of below 5.5 ft while 50 % of young adults in Brgay 6-C have heights of above 5.5 ft. 2. The mean of weekly sales Ana’s Sira-Sira store is P7,000. Answer: This means that most of the days in a week, the sales of Ana’s Sira-Sira store is P7,000. 3. The mode of street food in Davao City is “isaw”. Answer: This means most food vendors in the street sell “isaw”.

VI.

In a math quiz of 40 items, the mean score of the students is 32. a. The teacher missed to include one student with a score of 31. The mean score will be computed again to include the score 31, will the mean score increase? decrease? remains the same? Answer: The mean score will remain the same since the score 31 to be included has a very small difference with the existing mean. b. What if the score of one student is 20 not 31. Will the new mean increase? Decrease? remains the same? Answer: The mean score will decrease since the score 20 has a big difference with the existing mean.

c. What if the score of one student is 39 not 31. Will the new mean increase? Decrease? remains the same? Answer: The mean score will increase since the score 39 has a big difference with the existing mean. VII.

The score of students in an exam are 81, 83, 88, 90, 95, 96, 97, and 98. a) How will you find the median? Answer: Arrange the scores from smallest to highest or from highest to smallest then look for the middlemost score. In this case, the median is in between 90 and 95. Add the two scores then divide by 2 to get the median score. b)

What is the median score? Answer: The median score is 92.5. Solution: (90+95)÷ 2 = 92.5

c) If I will change the score 83 to 87, what is the median score? Answer: The median score is still the same (92.5). d) If I will add a score 100 in the set of data , what will be the median score? Answer: The median score is 95. This will be the middlemost score. 81, 83, 88, 90, 95, 96, 97, 98, 100

VIII.

The mean of 8 numbers is 70. What is the sum of these 8 Solution: 8x70= 560 / numbers? Answer: 560 560÷8=70 (mean is 70) The mean grade of 30 first year students is 90 and the mean grade of 23 second year students is 87. What is the mean grade of 53 students? Answer: The mean grade of the 53 students is 88.7 Solution: 30x90= 2700 23x87= 2001 2700+2001 = 4701 4701÷ 53 = 88.7 ( 53 students in all)

IX.

In this data set, 40, 48, 56 , 65, 70, 83, 92, 95, 110. a) If I will add 90 in the data set, what will happen to the range? Answer: The range is the same . The range will not be affected since the additional score is in between the lowest and highest scores. Range = Highest score – lowest score or 110 - 40 = 70 The range is 70.

b) If I will add 38 in the data set, what will happen to the range? Answer: There will be changes in the range, because the additional score is beyond the extreme score. The range : 110-38 = 72. X.

a) Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean. If the standard deviation is zero, what does it mean? b) Each of the following data sets has a mean of 10. i) 8, 9, 10, 11, 12 ii) 7, 9, 10, 11, 13 iii) 7, 8, 10, 12, 13 (hint: consider how far are the scores from the mean) b.1) Without doing any computations, which data set has the smallest standard deviation? Answer: Data set I ( the first data set) b.2) Without doing any computation, which data set has the largest standard deviation? Answer : Data set ii ( the third data set) c) Consider this data s ets: i) 6, 8, 10, 12, 14, 16, ----the mean is 11 ii) 3, 4, 4, 11, 20 ,24 ----- the mean is 11 c.) Looking into the given numbers of the data set, which data set has larger standard deviation? Without doing any computation, how did you know it? Answer: In second data set, the numbers far from the mean 11 when compared to the numbers in the first data set. The second data set will have a larger standard deviation when compared to the first data set. d) Compute the standard deviation of the data set: 9, 8, 7, 6, 8, 7, 5 Answer: The standard deviation is equal to 1.3 ....