Unit 1: Exploring One-Variable Data and Collecting Data

22 terms. Say what each one means, then open the card to check.

• Categorical variable

  A variable that places each individual into a group or category, such as a color, a brand or a yes-or-no answer.

  Example. Recording each fictional customer's preferred payment method (cash, card or phone) gives a categorical variable.

• Quantitative variable

  A variable whose values are numbers that count or measure something, so that averaging them or finding differences makes sense.

  Example. The number of minutes each student spends on the bus is quantitative, so a mean commute of 18 minutes is meaningful.

• Discrete variable

  A quantitative variable that can take only separate, countable values, often whole numbers, with gaps between possible values.

  Example. The number of siblings a student has can be 0, 1 or 2, but never 1.4.

• Statistical question

  A question that can be answered with data and expects the data to vary from one individual to the next.

  Example. How many hours do students at one school sleep on a school night is statistical, but how long one student slept last night is not.

• Distribution

  A description of what values a variable takes and how often it takes each one, shown in a table or a graph.

  Example. A dotplot of 25 fictional quiz scores shows the distribution: most scores sit between 7 and 9, and one score is 2.

• Skewed right

  A shape in which most values are low and a long tail stretches toward the high values on the right of the graph.

  Example. Household incomes in a fictional town are skewed right: most are modest, and a few very high incomes form a long right tail.

• Relative frequency

  The fraction or percent of all individuals that fall in one category or interval: the count for it divided by the total.

  Example. If 12 of 40 fictional students walk to school, the relative frequency of walking is 12/40, or 30 percent.

• Median

  The middle value of a data set put in order, or the mean of the two middle values when the count is even.

  Example. For the values 3, 5, 8, 10 and 41, the median is 8, the third of five values in order.

• Standard deviation

  A measure of variability that gives roughly the typical distance of the values from their mean.

  Example. Two fictional classes both average 75 points, but one class's standard deviation is 4 points and the other's is 12, so its scores spread much more.

• Interquartile range (IQR)

  The third quartile minus the first quartile: the length of the interval that holds the middle half of the data.

  Example. If Q1 is 20 minutes and Q3 is 35 minutes, the IQR is 15 minutes, so the middle half of the times span 15 minutes.

• Resistant measure

  A summary statistic that an extreme value barely changes; the median and IQR are resistant, but the mean, standard deviation and range are not.

  Example. Changing the largest of nine prices from 50 to 500 dollars leaves the median the same but raises the mean by 50 dollars.

• Five-number summary

  The minimum, first quartile, median, third quartile and maximum of a data set; a boxplot draws these five values.

  Example. A fictional set of reaction times has the summary 0.18, 0.22, 0.25, 0.29 and 0.41 seconds.

• 1.5 × IQR outlier rule

  A value is called an outlier if it lies more than 1.5 IQRs below the first quartile or more than 1.5 IQRs above the third quartile.

  Example. With Q1 = 10, Q3 = 18 and IQR = 8, any value above 18 + 12 = 30 or below 10 - 12 = -2 counts as an outlier.

• z-score

  How many standard deviations a value lies above or below the mean: the value minus the mean, divided by the standard deviation.

  Example. A score of 88 on a test with mean 80 and standard deviation 4 has a z-score of 2, two standard deviations above the mean.

• Simple random sample

  A sample chosen so that every possible group of that size from the population has the same chance of being the sample.

  Example. A club numbers its 400 members, and a random number generator picks 25 different numbers to choose who gets surveyed.

• Stratified random sample

  A sample made by splitting the population into groups of similar individuals, called strata, and taking a random sample from every stratum.

  Example. A college picks 20 students at random from each of its four class years to make a sample of 80.

• Cluster sample

  A sample made by splitting the population into groups, randomly choosing some whole groups, and surveying everyone in the chosen groups.

  Example. An inspector randomly picks 6 of a warehouse's 50 shelves and checks every box on those 6 shelves.

• Voluntary response bias

  Bias that arises when people choose themselves to answer, so those with strong opinions, often negative, are overrepresented.

  Example. A website poll about a new parking fee draws mostly angry drivers, so it overstates how many residents oppose the fee.

• Nonresponse bias

  Bias that arises when some people chosen for a sample cannot be reached or refuse to answer, and they differ from those who do answer.

  Example. Busy parents in a randomly chosen sample ignore a long survey, so the results underrepresent families with little free time.

• Confounding variable

  A variable related to both the explanatory variable and the response, so its effect cannot be separated from the effect being studied.

  Example. Students who choose to use a tutoring center may also be more motivated, so motivation is confounded with tutoring.

• Random assignment

  Using a chance process to decide which experimental units get which treatment, so the groups tend to be roughly alike apart from the treatment.

  Example. Drawing names from a hat to decide which 30 of 60 volunteers get a new stretching routine and which get the usual one.

• Blinding

  Keeping subjects, or the people measuring the response, from knowing which treatment each subject got; double-blind means both are kept unaware.

  Example. Neither the runners nor the coach timing them know who drank the new sports drink and who drank a look-alike.