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The manager went over the sales of mobile phones at the store and found that the mean sale was 45, with a standard deviation of 4. On a particular day, 52 mobile phones were sold. What is the z-score of the sale of mobile phones on that day? -28 28 1.75 -1.75 RATIONALE Recall that the z-score can be calculated with the following formula: The given value is 52 phones, the mean is 45 phones, and the standard deviation is 4 phones. Plug these values in to get the following z-score:
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The manager went over the sales of mobile phones at the store and found that the mean sale was 45, with a standard deviation of 4. On a particular day, 52 mobile phones were sold.
What is the z-score of the sale of mobile phones on that day?
Recall that the z-score can be calculated with the following formula:
The given value is 52 phones, the mean is 45 phones, and the standard deviation is 4 phones. Plug these values in to get the following z-score:
This also tells us that 52 is 1.75 z-scores or standard deviations above the mean.
In a poll of 300 preschoolers, 125 said they preferred chocolate ice cream, 71 said they preferred vanilla, 100 said they preferred cookies & cream, and 4 said they had never eaten ice cream.
If a pie chart were to be made showing the preference for each flavor, the central angle for the chocolate ice cream sector would be.
Recall that to get the angle for something in a pie chart we use the following formula:
open parentheses fraction numerator v a l u e over denominator t o t a l space v a l u e end fraction close parentheses times 360 degree
So in this case, the central angle for the chocolate ice cream sector would be:
A distribution in which one value is more frequent than other values.
A distribution in which numerous values are more frequent than other values.
Recall the mode is the most frequently occurring value. If a distribution is unimodal, it simply means there is one value that occurs most frequently.
Choose the statement that correctly describes a normal distribution.
Approximately 68% of the values are greater than the mean value.
The approximate percent of values lying within three standard deviations of the mean is 49.85%.
Approximately 68% of the values lie within one standard deviation of the mean.
The approximate percent of values lying within two standard deviations of the mean is 47.5%.
The normal distribution follows the empirical rule. This tells us that within one standard deviation of the mean, we should find roughly 68% of the data.
Sara wonders what percentage of her students answered at least half of the quiz questions incorrectly.
The relative cumulative frequency of students who earned a score of 20 or lower on the quiz is .
To get the relative frequency of 20 or lower, we need to find the cumulative number of 20 or less. We simply add up any bin that has the number 20 or less, such as the bin that shows scores of 1-5, 6-10, 11-15, and 16-20.
This would be:
Since there are an odd number (n=9) of values we simply take the middle, which is 62 mph.
Which of the following statements is true?
For a large enough sample size, the Central Limit Theorem states that the sample medians of repeated samples of a population are normally distributed.
For the Central Limit Theorem to be true, you must have a large sample, the underlying population must be normally distributed, and the standard deviation should not be finite.
Even with a very large sample size, the Central Limit Theorem states that the sample means of repeated samples of a population cannot be normally distributed.
For a large enough sample size, the Central Limit Theorem states that the sample means of repeated samples of a population are normally distributed.
The Central Limit Theorem gives us information about the properties' sampling distributions of statistics to have given that the sample size is large enough. It tells us the sampling distribution's mean should be equal to the true population mean.
The weekly salaries of full-time and part-time employees at a company are listed on the table.
What does the circled section represent?
Sixty-eight full-time employees earn $34 per week.
Two full-time employees earn more than $680 per week.
Thirty-four part-time employees earn more than $680 per week.
Two part-time employees earn between $680 and $690 per week.
If we recall that the stem and leaf can give us the actual values in the data set, then the circle corresponds to $683 and $684. We can then note that there are two part-time workers who make between $680 and $690.
Recall the variance and standard deviation of a standard normal are both 1, so the difference is 0.
The percent-change graph in the figure shows the change in Gross Domestic Product (GDP) from 2008-2012.
Which segment of the graph indicates the greatest increase in GDP growth?
Since the graph shows growth rate, the greatest growth rate will be the segment with the greatest slope that is positive. This is at segment B, where the growth rate increases from -0.5 to 2.
Select the statement that is FALSE.
The interquartile range is the difference between the highest and lowest values in the middle of a data set.
The range is the difference between the largest and smallest values of a data set.
The range is never greater than the greatest value of a data set.
The mean is never greater than the greatest value of a data set.
If we recall, the range is the maximum value minus the minimum value. Suppose in a given dataset, the maximum value is 20 and the minimum value is -5. Then the range is equal to:
The range of 25 is larger than the maximum value of 20, so the range can certainly be larger than the max value.
Which of the following statements about the stack plot is true?
More girls than boys chose English as their favorite subject.
Most of the students chose English as their favorite subject.
More than half the girls chose science as their favorite subject.
More boys chose math as their favorite subject than science.
When examining English, we can see that the darker area (girls) is much larger than the boys. So it is true that more girls choose English as their favorite subject. In fact, in all subjects it appears that there are more girls relative to boys.
Jerry graded seven standardized tests with the following scores:
Which standardized test score represents the 50th percentile?
The 50th percentile will be the median, or middle number. Make sure to first order the data.
The middle number is the 4th value, or 74.
The dotplot below shows the number of text messages received by a group of students in a day.
How many students received less than 15 messages?
In which of these cases should mode be used?
When the data is qualitative and we talk about the most frequent category
When the data is represented using ratio scale
When the data is represented using interval scale
When the data has extreme values
If the data is qualitative, it is only descriptive. In this case, the mode is a good measure since the mode examines the most frequently occurring value. The data can be non-numeric.
Consider this histogram showing the number of students in grade five who have one or more pets.
What is the difference in the number of students with the most and least numbers of pets?
The most number of pets is 10 and there is 1 person who has this many pets. The least number of pets is 1 and there are 5 people with 1 pet. So the difference in the number of people would be:
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he locates the mean and median time.
Which component of data analysis is Ralph utilizing?
An outlier in the data set
The center of the data set
The overall shape of the data
The overall spread of the data
Recall that the mean and median are measures of center. So by examining this, Ralph is looking at the center of the data.
Recall that if the data is normal, then the 68-95-99.7 rule applies which states that 68% of all data points fall within one standard deviation of the mean, 95% of all data points fall within two standard deviations of the mean, and 99.7% of all data points fall within three standard deviations of the mean.
5.3 cm and 5.7 cm are both 0.2 cm from the mean of 5.5 cm, which is the same as two standard deviations (0.1cm * 2) in either direction. This tells us that 95% of the data should lie between 5.3 cm to 5.7 cm.
Which of the following statements is true for an outlier?
It is a data point that is below or above Q3 ± 1.5 x IQR.
It is a data point that is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR.
It is a data point that is below or above Q1 ± 1.5 x IQR.
It is a data point that is between Q1 + 1.5 x IQR and Q3 - 1.5 x IQR.
To find an outlier we note the lower bound and upper bound for outliers are Q1 - 1.5IQR and Q3 + 1.5IQR respectively.
We can first calculate the variance of the data, , by using the part of the formula under the square root:
The formula for the standard deviation of a sample is:
Select the true statement for the following data set that has a mean of 6.75:
Answer choices are rounded to the hundredths place.
The variance is 6.75 and the standard deviation is 6.25.
The variance is 6.25 and the standard deviation is 2.50.
The variance is 2.50 and the standard deviation is 6.50.
The variance is 4.71 and the standard deviation is 2.17.
Next, we can find the standard deviation, , by simply taking the square root of the variance:
We can also use the statistical functions in Excel to quickly find the variance and standard deviation.
