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: What is the mean for each group?
PART B: What is the median for each group?
PART C: Which measure best describes the center of the data for each group? why?
PART A: I got... GROUP A=256
GROUP B=260
PART B: I got... GROUP A=245
GROUP B=246
However, I am not sure what PART C is asking me. PLEASE HELP ME ON PART C AND EXPLAIN WHY YOU GOT YOUR ANSWER!!!
Probably mean because it is the average and thus in total the exact center of each group.
Group b is 260
Great job on finding the mean and median for each group! Now let's move on to Part C.
Part C is asking which measure, mean or median, best describes the center of the data for each group and why.
To determine the center of the data, we need to consider the spread of the values in each group.
For Group A, the values range from $214 to $312, with a mean of $256 and a median of $245. The mean takes into account all the values in the dataset and is influenced by extreme values, in this case, the highest earning of $312. On the other hand, the median is the middle value of the ordered dataset and is not affected by extreme values.
For Group B, the values range from $215 to $310, with a mean of $260 and a median of $246. As in Group A, the mean is influenced by the highest earning of $310, while the median is not affected by extreme values.
In this case, both groups have similar spreads, but Group A has a slightly higher range, indicated by the higher maximum value. However, the median values for both groups are relatively similar, only differing by one dollar.
Considering the spreads and the fact that the medians are not significantly different, it can be argued that the median is a more appropriate measure for describing the center of the data in both groups. The median provides a more stable representation of the typical earnings among the part-time employees, regardless of extreme outliers.
To answer Part C, we need to determine which measure, either mean or median, best describes the center of the data for each group.
The mean is the average value of a set of data, while the median is the middle value when the data is arranged in order.
For Group A:
- The mean is $256: To find the mean, you add up all the values in the group and divide it by the total number of values (7 in this case). The sum of all values in Group A is $1792 ($245 + $224 + $218 + $295 + $214 + $312 + $284), and when you divide it by 7, you get $256 as the mean.
- The median is $245: To find the median, you arrange the values in ascending order. The middle value in Group A is $245.
For Group B:
- The mean is $260: Similar to Group A, you sum up all the values in the group and divide it by the total number of values (7). The sum of all values in Group B is $1700 ($223 + $230 + $310 + $246 + $295 + $301 + $215), and when divided by 7, you get $260 as the mean.
- The median is $246: Arrange the values in ascending order and find the middle value, which is $246.
Now, to determine which measure best describes the center of the data for each group:
For Group A, the mean ($256) is slightly higher than the median ($245). This suggests that there might be some larger values in the upper end, causing the mean to be pulled up. So, the mean might not be a perfect representation of the center for Group A.
For Group B, the mean ($260) is also slightly higher than the median ($246). Similar to Group A, this indicates that there might be some larger values towards the upper end, affecting the mean. So, like Group A, the mean may not fully represent the center for Group B.
In summary, for both groups, the median is a better descriptor of the center of the data as it is less influenced by extreme values. However, since the differences between the mean and median are relatively small in both cases, the effect of extreme values might not be significant.