Here's a frequency distribution table for the speeds of a sample of automobiles.
Speed(MPH) Frequency Midpoint(I found)
50-54 2 52
55-59 4 57
60-64 5 62
65-69 10 67
70-74 9 72
75-79 5 77
I am trying to find the variance but whatever I do I can't seem to find the answer.
The choices are
c.48.570
d.50.00
Using the midpoints of each interval, to find the mean first = sum of scores/number of scores.
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
To find the variance, you can follow these steps:
Step 1: Calculate the mean (average) of the data set.
- To do this, multiply each midpoint by its corresponding frequency, and then sum up the results.
- In this case, the midpoints are 52, 57, 62, 67, 72, and 77, and the frequencies are 2, 4, 5, 10, 9, and 5, respectively.
Mean = (52*2 + 57*4 + 62*5 + 67*10 + 72*9 + 77*5) / (2 + 4 + 5 + 10 + 9 + 5)
Step 2: Calculate the squared deviations from the mean.
- Take each midpoint, subtract the mean, and square the result.
- Then multiply each squared deviation by its corresponding frequency, and sum up the results.
Squared Deviations = [(52 - Mean)^2 * 2 + (57 - Mean)^2 * 4 + (62 - Mean)^2 * 5 + (67 - Mean)^2 * 10 + (72 - Mean)^2 * 9 + (77 - Mean)^2 * 5]
Step 3: Calculate the sum of the frequencies.
Sum of Frequencies = 2 + 4 + 5 + 10 + 9 + 5
Step 4: Calculate the variance.
- Divide the sum of squared deviations by the sum of frequencies minus 1.
Variance = Squared Deviations / (Sum of Frequencies - 1)
By applying these steps, you should be able to find the variance.