The table below shows the weekly earnings of two groups of employees working part-time at a local grocery store.
GROUP A:$245, $224, $218, $295, $214, $312, $284
GROUP B:$223, $230, $310, $246, $295, $301, $215
PART A: Which measure best describe the center of the data for each group? Why?
Is your choice between median and mean?
What is your answer? Why?
The median for GROUP A i got 245 and the median for GROUP B i got 246. Then the mean for GROUP A i got 256 and the mean for GROUP B i got 260.
The part i don't understand is what it is asking me. What does it mean by "which measure best describes the center of the data for each group?"
Is it asking me wether the mean or median is the best measure for the center of the data?
If so wouldn't it be the median, since the median means middle and it is asking me for the center of the data?
To determine the measure that best describes the center of the data for each group, we need to calculate the mean and median for both Group A and Group B.
Mean Calculation:
To calculate the mean, we need to sum up all the values in each group and then divide by the total number of values in that group.
For Group A:
Sum = $245 + $224 + $218 + $295 + $214 + $312 + $284
= $1792
Mean = Sum / Total number of values in Group A
Mean = $1792 / 7
Mean ≈ $256
For Group B:
Sum = $223 + $230 + $310 + $246 + $295 + $301 + $215
= $1820
Mean = Sum / Total number of values in Group B
Mean = $1820 / 7
Mean ≈ $260
Median Calculation:
To calculate the median, we need to arrange the values in each group in ascending order and find the middle value.
For Group A:
Arranged values: $214, $218, $224, $245, $284, $295, $312
Median = Middle value
Median = $245
For Group B:
Arranged values: $215, $223, $230, $246, $295, $301, $310
Median = Middle value
Median = $246
Conclusion:
For Group A, the mean is approximately $256, and the median is $245. Since the mean is close to the median, it suggests that the data is evenly distributed, making the mean a good measure of the center for Group A.
For Group B, the mean is approximately $260, and the median is $246. Since the mean is slightly higher than the median, it suggests that there might be some outliers or higher values in the data, making the median a better representation of the center for Group B.
Therefore, for Group A, the mean is the better measure of center, and for Group B, the median is the better measure of center.