3-1 SmartBook Assignment: Chapter 4 (Sections 4.1 through 4.5)

Pat's time in the 1600 meter run placed Pat in the 85th percentile in the school. What percentage of students are faster than Pat?

15 math: subtract 100%-85%. About 15% are faster. Pat is faster than 85%.

The following data set: 4, 6, 3, 5, has a range equal to

3

The median for the data set: 6, 4, 9, 5 is

5.5 EXPLANATION: Remember to put the data set in numerical order first. When the data set has an even number of observations, you must average the two middle values to find the median MATH: 4 5 6 9 (add the two middle values 5 + 6 = 11. Divide 11 by the number of digits you added (2) = 5.5

For the data set 4, 5, 6, and 9 the arithmetic mean is

6 math: Add the values together and divide by 4.

True or false: The standard deviation can be a negative value.

FALSE Reason: Because the standard deviation is based on squared differences it can never be negative.

Which of the following are measures of center of a data set?

Median Mode Mean

True or false: The arithmetic mean is the average of a data set.

TRUE

The mode for the data set: 4, 5, 6, 9 is

There is no mode

Which of the items below describes the usefulness of a standard deviation?

To gauge the relative position of data values within the data set.

To calculate the arithmetic mean

all of the data points must be added together, then divided by the number of data points.

When a data set is symmetrical the mean and median are approximately _____.

equal, same, identical, or similar (CHOOSE ONE)

Generally, the _____ is the best measure of center when outliers are present.

median

The best measure of central location for a numerical data set when the data set contains outliers is the _____.

median

When summarizing a qualitative data set the _____ is the best measure of central location.

mode

An owner of a grocery store wanted to determine the brands of soda that customers purchase at the store. When summarizing the data about soda brand purchase the meaningful measure of center is the

mode reason: The data set is qualitative

When a quantitative data set is significantly affected by _____, then the arithmetic mean is usually not a good measure of central location.

outliers, extremes, outlier, or extreme values (CHOOSE ONE)

A measure used to gauge the position of items within a data array is

standard deviation

Two widely used measures of dispersion are

the variance and the standard deviation.

In general, a data point is considered an outlier if it falls more than _____ standard deviations away from the average.

three or 3 CHOOSE ONE

The average squared difference of data values from their mean is the

variance

The sum of deviation from mean is always _____.

zero or 0 (CHOOSE ONE)

Calculate the standardized score for the following data value. Assume the mean = 100 and the standard deviation = 25: x = 60, z =

-1.6 (NEGATIVE ONE POINT SIX)

In which of the following data sets would the arithmetic mean not be a good measure of central location

0, 8, 8, 9, 10 Reason: The value "0" is an outlier for this data set

Standard deviations can be compared

1. For data sets with the same measurement units. 2. For data sets with the same measurement units and similar magnitude

Which of the following situations are valid reasons for removing an outlier from a data set?

1. If the data point was typed incorrectly into the spreadsheet. 2. If the observed value was taken from a population different from the one under study.

The interquartile range of a data set

1. Is calculated by subtracting the first quartile from the third quartile. 2. Represents the middle 50% of the data.

A box plot is constructed using several different values. Which of the following values from a data set are included in a box plot?

1. The largest value 2. The first quartile

A box plot is constructed using several different values. Which of the following values are included in a box plot

1. The second quartile 2. The third quartile 3. The smallest value

Which of the following statements is true?

1. Two data sets could have different means but the same standard deviation. 2. Two data sets could have the same mean but different standard deviations.

Which shape matches the mean and median relationship? 1. Left Skewed 2. Right Skewed 3. Symmetrical

1. mean < median 2. mean > median 3. mean = median

The second quartile is also the

1. median 2. 50th percentile

Match the data characteristic to what it describes. 1. CENTER 2. VARIABILITY 3. SHAPE

1. typical or middle value; where the data values are concentrated 2. spread of data values or dispersion 3. symmetrical or skewed

A certain value has a standardized score = 1.75. How many standard deviations from the mean does this value fall? Is this value greater than or less than the mean?

1.75. Greater than the mean. Reason: The z score tells how many standard deviations from the mean a data point falls. Reason: The positive z score means the data point is greater than the average.

Inner fences on a boxplot are _____ x IQR above Q3 and below Q1. Outer fences are _____ x IQR above Q3 and below Q1.

Blank 1: 1.5 Blank 2: 3

Quartiles divide the data into (choose a number) equal parts.

Blank 1: 4 or four CHOOSE ONE

The empirical rule states that approximately _____% of observations will fall within two standard deviations of the mean.

Blank 1: 95, 95.44, or 95.4 CHOOSE ONE NUMBER

When monitoring a process distribution, both the _____ and the _____ must be tracked.

Blank 1: center, mean, or average Blank 2: variability, dispersion, or variation CHOOSE ONE TERM FOR EACH BLANK

Randall Racer runs the 100 meter dash in an average time of 10.4 seconds with a standard deviation of 0.1 seconds. If Randall's times are normally distributed, we have a 99.7% expectation that his finishing time for his next race will be greater than ______ seconds.

10.1 Reason: 99.7% of values should fall within 3 standard deviations of the mean, not 2 standard deviations Reason: We have only a 50% expectation that his time will be greater than his average

The variance measures the average squared _____ from the _____.

Blank 1: deviations or differences Blank 2: mean or average (CHOOSE ONE TERM FOR EACH BLANK)

Numbers that summarize a sample of data are called _____ and numbers that summarize populations are called _____.

Blank 1: statistics Blank 2: parameters

The mode(s) for the data set: 4, 4, 5, 6, 9, 9 is

4 and 9 reason: Because these two numbers are the most frequent occurring data values.

If the median price for a home is $200,000, then _____% of homes cost less than $200,000.

50 reason: median means middle. If $200,000 is in the middle it is split in half.

For the data set 4, 5, 6, and 9 the arithmetic mean is

6 Math: add all numbers 4+5+6+9=24 and divide 24 by the amount of numbers you have (4) = 6

The median for the data set: 10, 6, 4, 9, 5 is .

6 Reason: order numbers from least to greatest 4, 5, 6, 9, 10 and choose the number in the middle.

The range for the data set: 2, 5, 5, 7, and 10 is

8 math: subtract largest number from the smallest number.

In a neighborhood there are five houses listed for sale for the following amounts: $250,000; $275,00; $280,000, $295,000, and $515,000. What is the best measure of center for the price of a house in the neighborhood?

MEDIAN

The best measure of central location when using a qualitative data set is the ______.

MODE Reason: The mean requires numerical calculation and the median requires that the data be ranked; therefore the mode works well for data that is not numerical.

The best measure of central location for a numerical data set when the data set contains outliers is the ______.

median