You are trying to be a YouTube star and are tracking the number of views on your videos. Below
are the number of views on your last 10 videos:
158, 164, 146, 170, 165, 187, 164, 174, 186, 197
a. Create a cumulative frequency table to represent the data:
Number of Views:
Frequency Cumulative:
Frequency:
b. Create a histogram to represent the data:
c. Find the mean, median, mode, and range of the data. Round to the nearest tenth if necessary:
d. Find the minimum, first quartile, third quartile, and maximum of the data. Round to the nearest tenth if necessary:
e. Create a box-and-whisker plot to represent the data:
f. Find the 40th percentile for the data set:
I NEED HELP ASAP I REALLY DO
XD may 4 2023 and still not answered
a. To create a cumulative frequency table, start by sorting the data in ascending order:
146, 158, 164, 164, 165, 170, 174, 186, 187, 197
Then, create two columns: "Number of Views" and "Cumulative Frequency."
Number of Views: Cumulative Frequency:
146 1
158 2
164 4
164 6
165 7
170 8
174 9
186 10
187 11
197 12
b. To create a histogram, you can count the frequency of each range of views and represent them as bars on a graph. Here's an example:
Frequency
| | 5
| |
| | 4
| |
| |
| | 3
| |
| |
| |
| | 2
| |
| |
| |
| | 1
| |
---------------------
145 160 175 190
c. To find the mean, median, mode, and range of the data:
Mean: Add up all the numbers of views and divide by the total number of videos:
(158 + 164 + 146 + 170 + 165 + 187 + 164 + 174 + 186 + 197) / 10 = 165.1 (rounded to the nearest tenth)
Median: Since there are 10 videos, the median is the average of the fifth and sixth numbers after sorting:
(165 + 170) / 2 = 167.5
Mode: The mode is the number that appears most frequently in the data set. In this case, there is no mode since all the numbers appear only once.
Range: The range is the difference between the highest and lowest numbers of views:
197 - 146 = 51
d. To find the minimum, first quartile, third quartile, and maximum:
Minimum: The smallest number in the data set is 146.
First Quartile: This is the median of the lower half of the data set. Since there are 10 videos, the first quartile is the average of the third and fourth numbers after sorting:
(158 + 164) / 2 = 161
Third Quartile: This is the median of the upper half of the data set. Since there are 10 videos, the third quartile is the average of the eighth and ninth numbers after sorting:
(186 + 187) / 2 = 186.5
Maximum: The largest number in the data set is 197.
e. To create a box-and-whisker plot, you need to determine the minimum, first quartile, median, third quartile, and maximum. Then, plot these values on a number line and draw a box from the first quartile to the third quartile.
Number Line: _____________________________________________________
|
|
|--------| |--------|
| |
Minimum First Quartile Third Quartile Maximum
f. To find the 40th percentile for the data set, consider the cumulative frequencies. The 40th percentile falls between the 4th and 5th observations. Interpolate the value using the formula:
40th percentile = L + ((N/100) * w)
where L is the lower boundary value of the group containing the 40th percentile, N is the cumulative frequency before the group, and w is the width of the group.
In this case, the group is [164, 165] with a cumulative frequency count of 6. The width of the group is 1.
40th percentile = 164 + ((40/100) * 1) = 164 + (0.4 * 1) = 164 + 0.4 = 164.4 (rounded to the nearest tenth)
Therefore, the 40th percentile for this data set is 164.4.
a. To create a cumulative frequency table, you need to count the number of videos that have up to a certain number of views. Start by sorting the number of views in ascending order:
146, 158, 164, 164, 165, 170, 174, 186, 187, 197
Then, for each number of views, count how many videos have up to that many views and write it in the "Cumulative Frequency" column. Also, write the frequency of each number of views in the "Frequency" column:
Number of Views: Frequency: Cumulative Frequency:
146 1 1
158 1 2
164 2 4
165 1 5
170 1 6
174 1 7
186 1 8
187 1 9
197 1 10
b. To create a histogram, you need to create intervals (bins) for the number of views and count how many videos fall into each interval. For this dataset, you could create intervals like 140-150, 150-160, 160-170, etc. Count the number of videos that fall into each interval and draw bars representing the frequency of each interval on a graph.
c. To find the mean, add up all the numbers of views and divide it by the total number of videos (10 in this case).
Mean = (158 + 164 + 146 + 170 + 165 + 187 + 164 + 174 + 186 + 197) / 10 = 169.1
To find the median, you first need to arrange the numbers in ascending order and then find the middle value. In this case, the median is the average of the fifth and sixth values:
Median = (165 + 170) / 2 = 167.5
To find the mode, you need to identify the number of views that appears most frequently. In this case, the mode is 164 since it appears twice.
To find the range, subtract the smallest value from the largest value:
Range = 197 - 146 = 51
d. To find the minimum, take the smallest value from the dataset, which is 146. The first quartile represents the 25th percentile. In this case, there are 10 videos, so the 25th percentile is the value at the 2.5th position when the data is sorted:
First Quartile = 146
The third quartile represents the 75th percentile. Again, there are 10 videos, so the 75th percentile is the value at the 7.5th position when the data is sorted:
Third Quartile = 186
To find the maximum, take the largest value from the dataset, which is 197.
e. To create a box-and-whisker plot, you need to represent the minimum, first quartile, median, third quartile, and maximum values on a number line. Draw a box around the first quartile, median, and third quartile values, and draw lines (whiskers) extending from the box to the minimum and maximum values.
f. To find the 40th percentile, you first need to order the data and find the value at the 40th percentile. In this case, the 40th percentile is the value at the 4th position when the data is sorted:
40th Percentile = 164
Remember, the percentile represents the value below which a given percentage of the data falls.