Score Quiz #7-One Quant. Var. Name: Part 1 STA 205-Wroughton Date: e interpretat

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Score Quiz #7-One Quant. Var. Name: Part 1 STA 205-Wroughton Date: e interpretation and units Directions: Answer each question fully-show all work and include appropriat Question: As some of you may have noticed, I wear a Fitbit. One of the things that this tracks is my steps per day. I took a random sample of days over the past few months in 2018 and recorded the number of steps per day and what day of the week it was. Use the histogram and summary statistics provided to help you answer the questions What two variables are recorded? For each, are they quantitative or categorical? (1 point) a. Variable Type (circle one) uate or Categerial Quantitative or Categorical How would you FULLY describe the shape of the graph? (0.5 point b. Column n Mean Std. dev. Median Min Max steps 41 13066 4479 14564 2962 20491 c For this problem would it be more appropriate to use Tchebycheff's rule or the Normal Curve Rule? Explain (0.5 point) Using the rule chosen in (c), calculate and interpret an interval that is 3 standard deviations from the mean. (1.5 points) d. MORE ON BACK

Explanation / Answer

Solution (a): Two variables are:

Solution (b): Shape of the distribution is left-skewed as it has a long left tail. Left-skewed distributions are also called negatively-skewed distributions. That’s because there is a long tail in the negative direction on the number line. The mean is also to the left of the peak.

Solution (c): The Empirical Rule(normal distribution) is an approximation that applies only to data sets with a bell-shaped relative frequency histogram. It estimates the proportion of the measurements that lie within one, two, and three standard deviations of the mean. While Chebyshev’s (Tchebycheff's) Theorem is a fact that applies to all possible datasets. It describes the minimum proportion of the measurements that lie must within one, two, or more standard deviations of the mean. For this left-skewed distribution, Tchebycheff's rule will be more appropriate.

Solution (d): Interval that is 3 sd from the mean is,

Lower limit = mean - 3*(standard deviation) = 13066 - 3*4479 = -371

Upper limit = mean +3*(standard deviation) = 13066 + 3(4479) =26503

As number of steps in a day can not be negative, then the interval that is 3sd from mean is [0, 26503]  

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