Interpreting Center & Variability.

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Presentation transcript:

Interpreting Center & Variability

Density Curves Smoothed-out histograms Always on or above the horizontal axis Area underneath = exactly one Shows the proportion of data values that fall within any interval Often used to describe the overall distribution

z-score Standardized score Creates the standard normal density curve m = 0, s = 1

What do these z-scores mean? -2.3 1.8 6.1 -4.3 2.3 s below the mean 1.8 s above the mean 6.1 s above the mean 4.3 s below the mean

Jonathan wants to work at Utopia Landfill Jonathan wants to work at Utopia Landfill. He must take a test to see if he is qualified for the job. The test has a normal distribution with m = 45 and s = 3.6. In order to qualify for the job, a person can not score lower than 2.5 standard deviations below the mean. Jonathan scores 35 on this test. Does he get the job? No, he scored 2.78 SD below the mean

Sally is taking two different math achievement tests with different means and standard deviations. The mean score on test A was 56 with a standard deviation of 3.5, while the mean score on test B was 65 with a standard deviation of 2.8. Sally scored a 62 on test A and a 69 on test B. On which test did Sally score the best? She did better on test A.

Normal Curve Bell-shaped, symmetrical curve Transition points between cupping upward & downward: m + s and m – s As s increases, the curve flattens & spreads As s decreases, the curve gets taller & thinner

Can ONLY be used with normal curves! Empirical Rule Approximately 68% of the data are within 1s of m Approx. 95% of the data are within 2s of m Approx. 99.7% of the data are within 3s of m See p. 180 Can ONLY be used with normal curves!

The heights of male students at GBHS are approximately normally distributed with a mean of 71 inches and standard deviation of 2.5 inches. a) What percent of the male students are shorter than 66 inches? b) Taller than 73.5 inches? c) Between 66 & 73.5 inches? About 2.5% About 16% About 81.5%

First, find the mean & standard deviation for the total setup time. Remember the bicycle problem? Assume that the phases are independent and are normal distributions. What percent of the total setup times will be more than 44.96 minutes? First, find the mean & standard deviation for the total setup time. Phase Mean SD Unpacking 3.5 0.7 Assembly 21.8 2.4 Tuning 12.3 2.7 2.5%