For which experiment are the elements of the dataset most likely to be measured in liters?(1 point)
Responses
Lora asks her neighbors how much water they drink each day.
Tracey asks her friends to estimate the weight of a bucket full of water.
Ingram asks the local fire department how long it takes them on average to put out a fire.
Thaddeus asks his friends how far they live from the local library.
Kwon records the low temperatures in degrees Celsius on 10 consecutive days. His dataset includes the following numbers:
18, 16, 21, 10, 10, 15, 12, 20, 17, 11
Kwon uses the template below to create a histogram with bins as shown.
----------------------------------------
10 14 18 22
Which bar will be the highest? Identify the range for the correct bar.
From: to just under: .
(1 point)
The bar that will be the highest is the one in the range from 10 to just under 14.
Is this correct?
Yes, that is correct!
Loren’s friends jump as far as they can and record their results in inches. Their results include the observations 42, 47, 50, 42, 45, 41, 49, 51, and 44. Which number, if added to the dataset, would represent an outlier in the data?(1 point)
Responses
40
44
72
52
Adding the number 72 to the dataset would represent an outlier in the data as it is significantly larger than the other values in the dataset.
Use the image to answer the question.
What are the values of the mean, median, and spread for the dataset shown in the bar graph?
(2 points)
The mean =
.
The median =
.
The spread =
.
It is not possible to determine the exact mean, median, and spread of the dataset shown in the bar graph without knowing the specific values of the data points. The graph only shows the frequency of each category, not the actual values themselves.
Use the table to answer the question.
Day of the Week Temperature
Sunday 45 degrees
Monday 52 degrees
Tuesday 44 degrees
Wednesday 62 degrees
Thursday 55 degrees
Friday 49 degrees
Saturday 50 degrees
Find the mean and median of the past week’s temperatures.
(1 point)
During the week, the mean temperature was
degrees.
During the week, the median temperature was
degrees.
To find the mean, we add all the temperatures and divide by the number of days:
Mean = [45 + 52 + 44 + 62 + 55 + 49 + 50] / 7 = 357 / 7 ≈ 51 degrees
To find the median, we need to arrange the temperatures in order:
44, 45, 49, 50, 52, 55, 62
Since there are an odd number of temperatures, the median is the middle one, which is 50 degrees.
Therefore:
During the week, the mean temperature was approximately 51 degrees.
During the week, the median temperature was 50 degrees.
Use the table to answer the question.
Game Free Throws Made
1 4
2 14
3 5
4 7
5 19
6 15
7 6
What value, the mean or median, best describes the shape of the data set that contains the number of free throws made by the basketball team? Choose 1 for mean and 2 for median.
(1 point)
It is difficult to determine which measure of central tendency (mean or median) best describes the shape of the data set without actually graphing or visualizing the data.
However, the presence of high values (such as 14, 15, and 19) and low values (such as 4 and 5) suggests that there may be outliers in the data, which could greatly affect the mean but not the median.
Therefore, the median may be a more appropriate measure of central tendency for this data set, as it is less affected by outliers.
So, we choose 2 for median.
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. What are the first and third quartiles?(1 point)
First quartile =
Third quartile =
To find the first quartile, we need to find the median of the lower half of the data set.
Lower half of the data set is: 2, 3, 5, 7, 11
The median of this data set is (5+7)/2 = 6.
Therefore, the first quartile is 6.
To find the third quartile, we need to find the median of the upper half of the data set.
Upper half of the data set is: 13, 17, 19, 23, 29
The median of this data set is (19+23)/2 = 21.
Therefore, the third quartile is 21.
So,
First quartile = 6
Third quartile = 21.
The highest temperatures measured at Death Valley, California, from 1995 to 2004 are given as a dataset.
127, 125, 125, 129, 123, 126, 127, 128, 128, 125
Find the range and the interquartile range of the dataset.
(1 point)
The range is
, and interquartile range is
.
To find the range of the dataset, we subtract the smallest value from the largest:
Range = 129 - 123 = 6
To find the interquartile range, we first need to find the median (second quartile) of the dataset.
We can arrange the data in order:
123, 125, 125, 125, 126, 127, 127, 128, 128, 129
The median of this dataset is the average of the middle two values, which are 126 and 127:
Median = (126 + 127) / 2 = 126.5
To find the first quartile (Q1), we take the median of the lower half of the data set:
Lower half of the data set is: 123, 125, 125, 125, 126
Median of the lower half of the data set is (125+125)/2 = 125.
To find the third quartile (Q3), we take the median of the upper half of the data set:
Upper half of the data set is: 127, 127, 128, 128, 129
Median of the upper half of the data set is (128+128)/2 = 128.
Therefore, the interquartile range (IQR) is:
IQR = Q3 - Q1 = 128 - 125 = 3
Therefore, the range is 6, and the interquartile range is 3.
Of the mean, median, and mode, which measure of center is most affected by outliers? Explain your reasoning including an example with at least 10 data points.
The mean is the measure of center most affected by outliers.
Outliers are data points that are significantly larger or smaller than the other values in the dataset. When calculating the mean, the values of all the data points are considered. Outliers can therefore greatly affect the value of the mean, as they can pull the mean towards their own value.
For example, consider the following dataset of 10 exam scores:
75, 65, 70, 80, 85, 95, 75, 70, 80, 90
The mean of this dataset is:
Mean = (75 + 65 + 70 + 80 + 85 + 95 + 75 + 70 + 80 + 90) / 10 = 78
Now imagine that one student’s score is changed from 95 to 30, which is a much lower score than the rest of the students. This student’s score is now an outlier.
The updated dataset is:
75, 65, 70, 80, 85, 30, 75, 70, 80, 90
The mean of this dataset is:
Mean = (75 + 65 + 70 + 80 + 85 + 30 + 75 + 70 + 80 + 90) / 10 = 72
We can see that the outlier has greatly affected the value of the mean, pulling it down by 6 points.
In contrast, the median and mode would not be as affected by an outlier because they are not based on all the values in the dataset. The median only relies on the middle value(s) of the dataset in order and the mode is simply the most frequently occurring value(s) in the dataset.