Step-by-step explanation:
Step 1: Arrange the data in ascending order:
0.1, 0.2, 0.2, 0.3, 0.5, 0.5, 0.5, 0.5, 0.5, 0.6, 0.7, 0.7, 0.8, 0.8, 0.9, 1.1, 1.3, 1.5, 1.7, 1.8, 1.8, 2.1, 2.2, 2.2, 2.5, 2.7, 3.1, 3.2, 3.2, 3.9, 4.3, 4.6, 4.7, 5.3, 6.5, 6.7, 8.8, 8.9, 9.1, 9.5, 9.5, 9.7, 10.5, 11.3, 11.3, 12.2, 13.5, 14.1, 14.1, 29.3
Step 2: Calculate P65 (the 65th percentile):
P65 is the value at which 65% of the data is below and 35% is above. To find P65, you can use the formula:
P65 = (65/100) * (N + 1)
Where N is the total number of data points (50 in this case).
P65 = (65/100) * (50 + 1)
P65 = (65/100) * 51
P65 = 33.15
So, P65 is the 34th data point in the ordered list.
P65 = 6.7 (rounded to one decimal place)
So, the 65th percentile (P65) is 6.7 Mbps.
Step 3: Find the percentile corresponding to 5.3 Mbps:
To find the percentile corresponding to 5.3 Mbps, you can use the following formula:
Percentile = (Number of values below x / Total number of values) * 100
Where x is the given data speed (5.3 Mbps).
First, count how many values are below 5.3 Mbps. There are 30 values below 5.3 Mbps.
Percentile = (30 / 50) * 100
Percentile = (3/5) * 100
Percentile = 60%
So, the percentile corresponding to 5.3 Mbps is 60%.
Step 4: Find Q1 (the 25th percentile):
Q1 is the value at which 25% of the data is below and 75% is above. To find Q1, you can use the same formula as for P65:
Q1 = (25/100) * (N + 1)
Q1 = (25/100) * (50 + 1)
Q1 = (25/100) * 51
Q1 = 12.75
So, Q1 is the 13th data point in the ordered list.
Q1 = 1.1
So, Q1 (the 25th percentile) is 1.1 Mbps.