E370 Stats - HW 2

What is the unit of measurement for the variance you calculated above? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166 $ $2 cents It does not have unit of measurement

$^2

If a data set has an even number of observations, the median must be equal to the mean cannot be determined is the average value of the two middle items is the average value of the two middle items when all items are arranged in ascending order

is the average value of the two middle items when all items are arranged in ascending order

When outliers are present in the data set, which measure is the best to describe central tendency in the data? weighted mean median mean standard deviation

median

What is the z-score for the data value $137 in this sample? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

-0.2007

Is it possible for a data set to have more than one mode? Yes, if two or more values in a data set occur the same number of times. Yes, if there are at least two different values in a data set, there is always more than one mode. Yes, if two or more values in a data set occur with the most frequency. No, there must always be a single mode, or else there is no mode.

Yes, if two or more values in a data set occur with the most frequency.

The standard deviation of a sample of 100 elements taken from a very large population is determined to be 60. The variance of the population cannot be larger than 3600 cannot be larger than 60 can be any value greater than zero must be at least 100

can be any value greater than zero

What is the median number of restaurant visits in the sample? 2 1 0 2 0 2 1 2 0 2 1 2

1.5

What is the value of the 1st quartile for this sample? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

129

What is the 40th percentile for this sample? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

134.6

What is the value of the median for this sample? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

139

What is the value of the mean for this sample? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

142

What is the mode in the sample? 2 1 0 2 0 2 1 2 0 2 1 2

2

What is the range of restaurant visits per week? 2 1 0 2 0 2 1 2 0 2 1 2

2

The following table shows a frequency distribution of the number of MacBook Air laptops sold per day at a particular Best Buy: Number of LaptopsFrequency 021124354252 What is the mean number of MacBook Air laptops sold per day? (Round your answer to 3 decimal places)

2.625

In 2009, the average donation to the Help Way was $225 with a standard deviation of $45. In 2010, the average donation was $400 with a standard deviation of $60. In which year did the donations show a more dispersed distribution? Hint: to answer this question, you need to calculate the coefficient of variation for each year. The donations show a more dispersed distribution in ___because the coefficient of variation is _____ for that year.

2009, larger

Using the sample data, it was computed that the 60th percentile for this data is $143.4. Calculated 60th percentile is best interpreted as: 60% of all gift spending for the Mother's Day are below $143.4 Middle 60% of gift-buyers spend on average $143.4 for the Mother's Day Middle 60% of gift-buyers spend less than $143.4 for the Mother's Day 60% of all gift spending for the Mother's Day are above $143.4 $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

60% of all gift spending for the Mother's Day are below $143.4

What is the value of the variance for this sample? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

620.9091

Using the sample data, it was computed that the 3d quartile for this sample equals $161.5. This is best interpreted as: The average for the middle 75% of spending for the Mother's Day equals $161.5 25% of spending for the Mother's Day are below $161.5 75% of spending for the Mother's Day are below $161.5 Middle 75% of spending for the Mother's Day are below $161.5 $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

75% of spending for the Mother's Day are below $161.5

racking system (compared to the offices without a tracking system)? It is hard to conclude anything because there are offices without a tracking system which have waiting times lower compared to some office with a tracking system On average, the offices without a tracking system are more efficient A tracking system does not help accommodating patients in a more efficient way which can be concluded because the average and the median wait times, and the standard deviation of the waiting times for the offices with the tracking system are higher A tracking system helps accommodating patients in a more efficient way which is supported by the lower average and median wait times, as well as the lower standard deviation of the waiting times

A tracking system helps accommodating patients in a more efficient way which is supported by the lower average and median wait times, as well as the lower standard deviation of the waiting times

How do we find the median if the number of observations in a data set is odd? By averaging the minimum and maximum values By taking the middle value in the sorted data set after eliminating outliers By averaging the first and the third quartiles By taking the middle value in the sorted data set

By taking the middle value in the sorted data set

Consider patients with a wait time of 37 minutes in the samples of offices with and without a wait tracking system (10th and 6th patient in the data, respectively). Comparing the z-scores for these two patients, what would you conclude? The z-score is lower for the patient in the sample of offices without a tracking system because the median is lower in this sample Even though the wait time is the same for these patients, the z-scores are different because the patients belong to the samples with different means and standard deviations The z-scores are the same because the wait times are the same Even though the wait time is the same for these patients, the z-scores are different because we look at different observations in the corresponding samples - 10th vs 6th patient, respectively

Even though the wait time is the same for these patients, the z-scores are different because the patients belong to the samples with different means and standard deviations

Which of the following is the most influenced by outliers? Mean 1st quartile Median 75th percentile

Mean

The Boom company has recently decided to raise the salaries of all employees by 10%. Which of the following is(are) expected to be affected by this raise? Mean and mode only Mode and median only Mean and median only Mean, median, and mode

Mean, median, and mode

If two groups of numbers have the same mean, then their standard deviations must also be equal their modes must also be equal their medians must also be equal None of the suggested alternatives is correct

None of the suggested alternatives is correct

The mean of the sample is always smaller than the mean of the population from which the sample was taken None of the suggested alternatives is correct can never be negative can never be zero

None of the suggested alternatives is correct

Using the sample data, it was computed that the z-score for a data value of $166 is 0.96. Calculated z-score is best interpreted as: Spending of $166 is 0.96 standard deviations away from the mean spending Spending of $166 is 96% above the mean spending Spending of $166 is 0.96 above the mean spending Spending of $166 is 0.96 standard deviations above the mean spending $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166

Spending of $166 is 0.96 standard deviations above the mean spending

Which one of the following statements is true for a right-skewed distribution? The mean is less than the median. The mean is roughly equal to the median. The mean is greater than the mode. The mean is greater than the median.

The mean is greater than the median.

What is the value of the mode for this sample? $110 $132 $144 $172 $141 $102 $190 $137 $134 $148 $128 $166 The mode is the same as the median There are multiple modes The mode is the same as the mean The mode does not exist

The mode does not exist

Do the data for offices with and without a tracking system contain outliers? Hint: that's where you want to use the z-scores. Only the data for the offices without a tracking system contain outliers There are no outliers in the data Only the data for the offices with a tracking system contain outliers Both the data for the offices with and without a tracking system contain outliers

There are no outliers in the data

Comparing the consistency (variability) between two data sets when their means are very different is best done with the z-score standard deviation median coefficient of variation

coefficient of variation

Since the population is always larger than the sample, the value of the sample mean could be larger, equal to, or smaller than the true value of the population mean is always equal to the true value of the population mean is always smaller than the true value of the population mean is always larger than the true value of the population mean

could be larger, equal to, or smaller than the true value of the population mean

The median is defined as the closest value to the mean middle point in a data set average of a data set most frequent value of a data set

middle point in a data set

Which measure would you use to describe central tendency for qualitative data? mode mean median weighted mean

mode

During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten-day period cannot be computed since all the numbers are negative is negative since all the numbers are negative must be positive can be either negative or positive

must be positive

If the variance of a data set is correctly computed with the formula using n - 1 in the denominator, which of the following is true? the data set is a population the data set is a sample the data set could be either a sample or a population the data set includes all subjects of interest in the study

the data set is a sample

Which of the following symbols represents the mean of the sample? x¯ σ μ n

x¯

Which of the following statements is NOT true concerning the attributes of z-scores? z-scores are equal to zero for data values equal to the mean of the distribution z-scores are positive for data values above the mean of the distribution z-scores can be positive or negative for data values above the mean of the distribution

z-scores can be positive or negative for data values above the mean of the distribution

Which of the following symbols represents the standard deviation of the population? σ x¯ μ

σ

The variance of restaurant visits is calculated to be 0.75. What is the standard deviation of restaurant visits per week? (Please, round your solution to at least 2 digits). 2 1 0 2 0 2 1 2 0 2 1 2

0.866

What is the mean number of restaurant visits in the sample? (Please, do not round your answer). 2 1 0 2 0 2 1 2 0 2 1 2

1.25