Find the mean deviation about the mean of the following data of ages of married men in a certain town.
Ages 15-24:25-34 35-44 45-54 55-64 65-74
No. of Men 33 264 303 214 128 58
Mean = (15+25+35+45+55+65)/6 = 40
Deviation = (15-40) + (25-40) + (35-40) + (45-40) + (55-40) + (65-40)
= -25 + -15 + -5 + 5 + 15 + 25
= 0
Mean Deviation about the Mean = 0
Find the mean deviation about the mean of the following data of ages of married men in a certain town.
Ages 15-24 25-34 35-44 45-54 55-64 65-74
No. of Men 33 264 303 214 128 58
To find the mean deviation about the mean, follow these steps:
1. Find the mean (average) of the ages:
First, identify the midpoint of each age group:
Midpoint of 15-24: (15 + 24) / 2 = 19.5
Midpoint of 25-34: (25 + 34) / 2 = 29.5
Midpoint of 35-44: (35 + 44) / 2 = 39.5
Midpoint of 45-54: (45 + 54) / 2 = 49.5
Midpoint of 55-64: (55 + 64) / 2 = 59.5
Midpoint of 65-74: (65 + 74) / 2 = 69.5
Now, calculate the weighted mean by multiplying each midpoint by its respective frequency, summing them, and dividing by the total frequency:
(19.5 * 33 + 29.5 * 264 + 39.5 * 303 + 49.5 * 214 + 59.5 * 128 + 69.5 * 58) / (33 + 264 + 303 + 214 + 128 + 58)
2. Calculate the deviation for each age group:
Subtract the mean from each midpoint:
Deviation for 15-24: 19.5 - mean
Deviation for 25-34: 29.5 - mean
Deviation for 35-44: 39.5 - mean
Deviation for 45-54: 49.5 - mean
Deviation for 55-64: 59.5 - mean
Deviation for 65-74: 69.5 - mean
3. Calculate the absolute deviation for each age group:
Take the absolute value of each deviation calculated in step 2:
Absolute deviation for 15-24: |19.5 - mean|
Absolute deviation for 25-34: |29.5 - mean|
Absolute deviation for 35-44: |39.5 - mean|
Absolute deviation for 45-54: |49.5 - mean|
Absolute deviation for 55-64: |59.5 - mean|
Absolute deviation for 65-74: |69.5 - mean|
4. Calculate the weighted mean of the absolute deviations:
Multiply each absolute deviation by its respective frequency, sum them, and divide by the total frequency:
(|19.5 - mean| * 33 + |29.5 - mean| * 264 + |39.5 - mean| * 303 + |49.5 - mean| * 214 + |59.5 - mean| * 128 + |69.5 - mean| * 58) / (33 + 264 + 303 + 214 + 128 + 58)
This final result represents the mean deviation about the mean for the given data set of ages of married men in the town.
To find the mean deviation about the mean, we need to follow these steps:
Step 1: Calculate the mean of the data.
The mean is calculated by summing up all the values and dividing it by the total number of values. For this problem, we can use the midpoint of each age group as the value. Let's calculate the mean:
Mean = (15+24)/2 * 33 + (25+34)/2 * 264 + (35+44)/2 * 303 + (45+54)/2 * 214 + (55+64)/2 * 128 + (65+74)/2 * 58
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33 + 264 + 303 + 214 + 128 + 58
Step 2: Calculate the deviations of each value from the mean.
The deviation is the difference between the value and the mean. To find the deviation, subtract the mean from each value:
Deviation = |Value - Mean|
For example, to calculate the deviation for the first age group (15-24), subtract the mean from each value in the group:
Deviation for ages 15-24 = |(15+24)/2 - Mean| * 33
Similarly, calculate the deviations for the other age groups.
Step 3: Calculate the mean of the absolute deviations.
To find the mean deviation about the mean, we calculate the mean of the absolute deviations. To do this, add up all the absolute deviations and divide by the total number of values:
Mean Deviation = (Deviation for ages 15-24 + Deviation for ages 25-34 + Deviation for ages 35-44 + Deviation for ages 45-54 + Deviation for ages 55-64 + Deviation for ages 65-74)
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33 + 264 + 303 + 214 + 128 + 58
Follow these steps, and you will be able to find the mean deviation about the mean of the given data of ages of married men in a certain town.