QuestionCalculate the mean of the frequency distribution for speeds: 42-45 (22), 46-49 (12), 50-53 (7), 54-57 (4), 58-61 (2).
Studdy Solution
STEP 1
Assumptions1. The frequency distribution table represents the number of observations (frequency) for each speed interval.
. The midpoint of each interval is used to represent the interval for calculation purposes.
3. The mean is calculated as the sum of the product of the midpoint and frequency for each interval divided by the total frequency.
STEP 2
First, we need to calculate the midpoint for each speed interval. The midpoint is calculated as the sum of the lower and upper limit of the interval divided by2.
STEP 3
Calculate the midpoint for the first speed interval.
STEP 4
Calculate the midpoint for the second speed interval.
STEP 5
Calculate the midpoint for the third speed interval.
STEP 6
Calculate the midpoint for the fourth speed interval.
STEP 7
Calculate the midpoint for the fifth speed interval.
STEP 8
Now, we need to calculate the product of the midpoint and frequency for each interval.
STEP 9
Calculate the product for the first speed interval.
STEP 10
Calculate the product for the second speed interval.
STEP 11
Calculate the product for the third speed interval.
STEP 12
Calculate the product for the fourth speed interval.
STEP 13
Calculate the product for the fifth speed interval.
STEP 14
Now, we need to calculate the sum of the product of the midpoint and frequency for all intervals.
STEP 15
Calculate the sum of the products.
STEP 16
We also need to calculate the total frequency, which is the sum of the frequencies for all intervals.
STEP 17
Calculate the total frequency.
STEP 18
Finally, we can calculate the mean of the frequency distribution. The mean is calculated as the sum of the product of the midpoint and frequency for each interval divided by the total frequency.
STEP 19
Calculate the mean of the frequency distribution.
The mean of the frequency distribution is the result from step19.
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