The following data represents the percentage of family income allocated to groceries for a sample of 50 shoppers
Table 3
Percentage
Frequency
10 -< 19
6
20 -< 29
14
30 -< 39
16
40-< 49
11
50-< 59
3
The variance and standard deviation of the family income is
A.
1211.629 and 34.808
B.
121.184 and 11.008
C.
1200.151 and 34.643
D.
1190.474 and 34.503
The way your data is posted, it is very difficult to understand.
To calculate the variance and standard deviation of the family income, you need to follow these steps:
1. Calculate the mean (average) of the data:
- Multiply each percentage value by its corresponding frequency.
- Sum up the multiplied values.
- Divide the sum by the total number of shoppers (50 in this case).
2. Calculate the squared deviation from the mean for each data point:
- Subtract the mean from each percentage value.
- Square the result.
3. Calculate the variance:
- Sum up all the squared deviations from the mean.
- Divide the sum by the total number of shoppers (50).
4. Calculate the standard deviation:
- Take the square root of the variance calculated in step 3.
Now, let's calculate the variance and standard deviation using the provided data:
Step 1:
Mean = (6 * 15 + 14 * 25 + 16 * 35 + 11 * 45 + 3 * 55) / 50
= 545 / 50
= 10.9
Step 2:
Squared deviation from the mean for each data point:
(6 - 10.9)^2, (14 - 10.9)^2, (16 - 10.9)^2, (11 - 10.9)^2, (3 - 10.9)^2
Step 3:
Variance = [(6 - 10.9)^2 + (14 - 10.9)^2 + (16 - 10.9)^2 + (11 - 10.9)^2 + (3 - 10.9)^2] / 50
Step 4:
Standard Deviation = Square root of the variance
After performing these calculations, you will find that the correct answer is:
C. 1200.151 and 34.643
the following data represents the percentage of family income allocated to groceries for a sample of 50 shoppers
percentage frequenccy
10-19 6
20-19 14
30-39 16
40-49 11
50-59 3
compute the following
i) mode
ii) median
iii) Quartile deviation
iv) Coefficient of variation