1.2 - Measures of Central Tendency (Solutions)

1.2 - Measures of Central Tendency (Solutions) - 1.2...

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Unformatted text preview: 1.2 Measures of Central Tendency (Solutions) Section 1.2 Measures of Central Tendency MEAN POPULATION: the entire group under study SAMPLE: a subset of the population of interest. POPULATION sample X = N = Population Mean X, x = Individual Observation x = x = sample mean x n N, n = Total number of Observations 1 1.2 Measures of Central Tendency (Solutions) Ex: 11 random students were surveyed to see the number of Tim Horton's coffees they drank last week. Here are the results 5 7 2 4 5 2 7 8 5 6 4 Find the MEAN: x= 5+7+2+ 4 + 5+2+7+8+ 5+6+ 4 11 55 = 11 = 5 coffees MEAN The mean is the balance point of the data 1 2 3 4 5 6 7 8 9 -3 +1 The deviation from the mean is the distance of a point from the mean value Deviation from the mean = (x - x ) 2 1.2 Measures of Central Tendency (Solutions) MEAN TIM HORTON'S DATA x The sum of all the deviations from the mean is ALWAYS ZERO 2 2 4 4 5 5 5 6 7 7 8 X-X 2 5 = 3 2 5 = 3 4 5 = 1 4 5 = 1 5 5 = 0 5 5 = 0 5 5 = 0 6 5 = + 1 7 5 = + 2 7 5 = + 2 8 5 = + 3 (x - x ) 0 MEAN Data set 1: 2 2 4 4 5 5 5 6 7 7 8 Mean = 5 0 5 10 15 20 25 30 35 40 45 50 55 60 Data set 2: 2 2 4 4 5 5 5 6 7 7 58 Mean = 9.55 0 5 10 15 20 25 30 35 40 45 50 55 60 Is a mean of 9.55 an accurate measure of this central tendency? NO 3 1.2 Measures of Central Tendency (Solutions) MEDIAN STEP 1: Arrange #s from smallest to largest (an array) STEP 2: Find the median position = n + 1 2 STEP 3: Find the median ODD n median is the middle # EVEN n median is the mean of the 2 middle #s Ex: 11 random students were surveyed to see the number of Tim Horton's coffees they drank last week. Here are the results 5 7 2 4 5 2 7 8 5 6 4 Find the MEDIAN: STEP 1: Array: 2 2 4 4 5 5 5 6 7 7 8 STEP 2: Median Position: (11) + 1 = 6 2 STEP 3: Median: 5 4 1.2 Measures of Central Tendency (Solutions) MEDIAN Data set 1: 2 2 4 4 5 5 5 6 7 7 8 Mean = 5 Median = 5 0 5 10 15 20 25 30 35 40 45 50 55 60 Data set 2: 2 2 4 4 5 5 5 6 7 7 58 Mean = 9.55 Median = 5 0 5 10 15 20 25 30 35 40 45 50 55 60 Is a median of 5 an accurate measure of this central tendency? YES MODE A set of data may have: One Mode: 12 3 4 5 18 5 7 9 Mode = 5 No Mode: 72 87 65 94 88 91 77 Mode = N/A More than One Mode: 53 32 45 53 51 39 45 Mode = 45 and 53 5 1.2 Measures of Central Tendency (Solutions) Ex: 11 random students were surveyed to see the number of Tim Horton's coffees they drank last week. Here are the results 5 7 2 4 5 2 7 8 5 6 4 Find the MODE: Mode = 5 SKEWNESS Symmetrical: Values are evenly distributed Mean Median Mode Skewed: Most values are large with some extreme small values Mean < Median < Mode + Skewed: Most values are small with some extreme large values Mean > Median > Mode 6 1.2 Measures of Central Tendency (Solutions) PROS Mean CONS USE WHEN... ...data is QUANTITATIVE and NOT SKEWED Preferred Influenced by measure of extremes central tendency for quantitative data Median Less affected by Less preferred ...data is QUANTITATIVE and extremes if data is SKEWED symmetrical ...data is Can be used for May be no QUALITATIVE mode or QUALITATIVE multiple modes data Mode LAB QUESTIONS: Lab 1 # 3 7 ...
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