Find the mean of the data summarized in the given frequency distribution . Compare the computed mean to the actual mean of 57.6 Degrees.
Low Temperature ( F) 40-44 45-49 50-54 55-59 60-64 Frequency 2 5 9 6 3
The mean of the frequency distribution is ___
Find the middle of each interval
for 40 - 44 the middle is 42 multiply that by 2
do the same for each interval. Find the middle and multiply that number times the frequency.
Sum all of those results
To find the mean divide by 25
Compare with the actual computed mean given above.
To find the mean of a frequency distribution, you need to perform the following steps:
1. Create a table with columns for the intervals (low temperature in this case), the frequency, and a column for the midpoint of each interval.
Low Temperature (F) Frequency Midpoint
40-44 2 42
45-49 5 47
50-54 9 52
55-59 6 57
60-64 3 62
2. Calculate the product of each midpoint and its corresponding frequency. This will give you the "sum of the products".
Sum of the products = (2 * 42) + (5 * 47) + (9 * 52) + (6 * 57) + (3 * 62)
3. Calculate the sum of the frequencies.
Sum of the frequencies = 2 + 5 + 9 + 6 + 3
4. Divide the sum of the products by the sum of the frequencies.
Mean = Sum of the products / Sum of the frequencies
Now let's calculate the mean for the given frequency distribution:
Mean = (2 * 42) + (5 * 47) + (9 * 52) + (6 * 57) + (3 * 62) / (2 + 5 + 9 + 6 + 3)
Calculating the above expression, the mean comes out to be:
Mean = 549 / 25 = 21.96 Degrees
Now, to compare this computed mean to the actual mean of 57.6 degrees:
The computed mean (21.96 degrees) is significantly lower than the actual mean (57.6 degrees). Thus, the computed mean is not equal to the actual mean.