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:
a. Cumulative Frequency Table:
Number of Views: 158, 164, 146, 170, 165, 187, 164, 174, 186, 197
Frequency: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Cumulative Frequency: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55
b. Histogram:
Frequency
200 ┼
┤
180 ┼ ╮
┤ ║
160 ┼ ║
┤ ║
140 ┼ ║
┤ ║
120 ┼ ║
┤ ║
100 ┼ ║
┤ ║
80 ┼ ║
┤ ║
60 ┼ ║
┤ ║
40 ┼ ║ ╯
┤ ║
20 ┼ ║
┤ ║
0 ┼─╫─╫─╫─╫─╫─╫─╫─╫─╫─
1 2 3 4 5 6 7 8 9
c. Mean: 167.1
Median: 165.0
Mode: 164
Range: 51
d. Minimum: 146
1st Quartile: 161.5
3rd Quartile: 183.0
Maximum: 197
e. Box-and-Whisker Plot:
┌─────┐
197 ┼─────┼
┌─────┴─────┐
190 ┤ │
┤ ┌───┐ │
185 ┼─────┼ ┼─┼─────┐
┤ │ │ │ │
180 ┤ │ │ │ │
┤ │ │ │ │
175 ┤ │ │ │ │
┤ │ │ │ │
170 ┤ │ │ │ │
┤ ┼───┼─┘ │
165 ┤ │ │ │
┤ │ │ │
160 ┤ │ │ │
┤ │ │ │
155 ┤ │ │ │
└─────┴───┴───────┘
f. 40th percentile: 162.8
a. Cumulative Frequency Table:
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. Histogram:
Number of Views
200 |
190 |
180 |
170 | x x x
160 | x x x
150 |
140 | x
c. Mean: (158 + 164 + 146 + 170 + 165 + 187 + 164 + 174 + 186 + 197) / 10
= 173.1 (rounded to the nearest tenth)
Median: Since there are 10 data points, the median will be the average of the
5th and 6th data points.
(165 + 170) / 2 = 167.5
Mode: The mode is the value that appears most frequently in the data set.
In this case, there is no mode as each value appears only once.
Range: The range is the difference between the maximum and minimum values.
Maximum = 197
Minimum = 146
Range = 197 - 146 = 51
d. Minimum: 146
First Quartile: The first quartile is the median of the lower half of the data
set. Since there are 10 data points, the first quartile will be
the average of the 3rd and 4th data points.
(146 + 158) / 2 = 152
Third Quartile: The third quartile is the median of the upper half of the data set.
Since there are 10 data points, the third quartile will be
the average of the 7th and 8th data points.
(174 + 186) / 2 = 180
Maximum: 197
e. Box-and-Whisker Plot:
- Minimum: 146
- Median: 167.5
- First Quartile: 152
- Third Quartile: 180
- Maximum: 197
120 |
130 |
140 |
150 |---------|
160 | x x |
170 | x |
180 |---------|
190 |
200 |
210 |
a. To create a cumulative frequency table, we need to organize the number of views in ascending order and calculate the cumulative frequency.
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, we will use intervals of, for example, 10 views each.
Number of Views: Frequency:
140-149 0
150-159 2
160-169 4
170-179 1
180-189 2
190-199 1
c. Mean: To find the mean, sum up all the number of views and divide by the total number of videos.
Sum = 158 + 164 + 146 + 170 + 165 + 187 + 164 + 174 + 186 + 197 = 1715
Mean = 1715 / 10 = 171.5
Median: Arrange the number of views in ascending order, and find the middle value.
146, 158, 164, 165, 170, 174, 186, 187, 197
Since we have an even number of elements, we calculate the median by taking the average of the two middle values:
Median = (165 + 170) / 2 = 167.5
Mode: The mode is the value(s) that appears most frequently. In this case, there is no mode as each value occurs only once.
Range: Find the difference between the highest and the lowest value.
Range = 197 - 146 = 51
d. Minimum: The minimum is the smallest value, which is 146.
First Quartile: Arrange the number of views in ascending order and find the median of the lower half.
146, 158, 164, 165
Since we have an odd number of elements, the first quartile is the median of the lower half:
First Quartile = 158
Third Quartile: Arrange the number of views in ascending order and find the median of the upper half.
170, 174, 186, 187, 197
Since we have an odd number of elements, the third quartile is the median of the upper half:
Third Quartile = 186
Maximum: The maximum is the largest value, which is 197.
e. To create a box-and-whisker plot, we plot a number line and mark the minimum, first quartile, median, third quartile, and maximum.
___146_________________________158__167.5__186_____________________________197___
f. To find the 40th percentile, we need to find the value below which 40% of the data falls.
Since we have 10 data points, the 40th percentile is the 4th element when the data is arranged in ascending order:
146, 158, 164, 165
The 40th percentile is 165.